Here are some of my thoughts on some of the things we still don't know about Digimon Adventure tri. These are my personal theories and opinions, and there is nothing remotely official about any of this. It's just fun to speculate.
1. The meaning behind "tri."
Most likely, it's short for triangle.
On the one hand, it's a pun on the fact that it this the third series of Digimon Adventure. Similarly, 02 refers to the year in which the second series takes place — it is not an ordinal. Which is why it's completely wrong to call the other series "01" or "03". ETA: They probably also want to avoid any confusion with Tamers, which was known as "Digimon 3" in many markets.
On the other hand, it might be a clue about the plot. We've been told to pay attention to all the "threes" in the story. People have been speculating that we could be looking at some sort of "triple evolution" (like jogress evolution involving 3 characters), while others have brought up the idea that the series will focus on romantic triangles. Both theories create some interesting questions, but I feel that the former is much more likely.
2. Nade-nade
There are 2 batches of eggs left, which means we should get 2 sets of official announcements. Sora and Mimi's eggs should hatch in late January / early February. The final egg is Koushirou's, but we don't know when it would be put up on the website; most likely, it will hatch much closer to the premiere date.
Lots of people are expecting some sort of preview or trailer next, but I'm doubtful. To start with, with each egg we seem to get increasingly important announcements. If they release a full trailer with the penultimate eggs, how are they going to top that later? Personally, I find it more likely that we are getting the remaining silhouettes (including the digimon partners) plus the cast list and/or the premiere date. The trailer is still a possibility, of course, although I've read that anime trailers are usually released around a month before the start of a series. (Maybe someone who is more knowledgable about Japan can confirm this.)
With the final egg, the nade-nade thing will probably end. At that point, we will hopefully get a proper official website that includes official character profiles.
3. Premiere date, TV Channel, and timeslot
Nothing has been announced so far. Digimon Adventure and 02's former Fuji TV timeslot (Sundays, 9:00) is currently occupied by the final episodes of Dragonball Kai. We know tri will start in the Spring (so late April, at most), so in theory it could be replacing Dragonball Kai after it ends.
However, it's still unclear if Dragonball Kai will even finish in time. We could very well see tri. going to a different timeslot and/or channel. It would be a pity, since Fuji TV and its building play a prominent part in the Adventure canon (for example, Hiroaki, Yamato and Takeru's dad, works there).
4. Series length & Number of episodes
Considering that the previous series had 50+ episodes, and after all this hype, I admit that it would be disappointing if tri. was only 13 or 26 episodes. Still, and although no information has been released so far, we should all be prepared for the possibility of tri. being a single-arc short series. Honestly, it would not be surprised if it was conceived as a short 15th anniversary special rather than a full-blown, year-long epic like Adventure and 02. Either way, ideally tri becomes so successful that they'll give us a fourth series afterwards.
5. Genre
In his recent interview, producer Shuhei Arai said that they want tri. to appeal to grown-up fans. This, along with the updated character designs, the staff's résumé and the characters's ages, has lead some people to think tri. will be more of a "Slice of Life" anime, focusing on aspects like school life, relationships, and romance.
However, considering that the main purpose of Digimon anime has always been to sell merchandising, the idea that they will push aside the action-adventure and "digital monsters" aspect of the series seems far-fetched. While tri. might want to appeal to more sophisticated audiences, including western fans (let's not forget that anime for children is no longer as popular in the West as it was in the 90s) I doubt it will stop being a classic Digimon story. They want to cash in keep nostalgic adult fans, but they I don't think they'll alienate younger audiences completely.
6. The Cast
It seems very likely that most of the original cast will return. Over the years, the Adventure voice actors have reprised their roles in sporadic projects, such as the 2014 PSP game. Most recently, the Digimon Adventure Blu-ray Box (to be released on 03.03.2015) includes a brand new Drama CD that features the vast majority of the cast.
As it has been pointed out, the Drama CD has two notable absences: Toshiko Fujita (Taichi) and any of Takeru's voice actors. This means that either Taichi and Takeru will not appear in that story (strange, considering that Augumon and Patamon will) or that both characters might be getting new voice actors. Of course, no one knows if or how this will translate in tri. Personally, I'd love to see 14-year-old Takeru being voiced by Hirata Hiroaki, who plays Narrator/adult Takeru (and also appears in the CD Drama). As for Taichi, the creators might have decided that it was time for him to have a new (male) voice, even though Fujita's voice is very iconic. Time will tell.
7. The music
I'm sure everyone is expecting Kouji Wada, AiM, and Ayumi Miyazaki to sing a new Opening, Ending, and Insert Song (or a new version of the old ones). Considering that they performed on the event where Digimon Adventure tri. was annouced, I imagine that their participation in the new series is a strong possibility. AiM (Ai Maeda) is also Mimi's voice actor, so she seems the most likely candidate.
Another interesting question concerns the serie's instrumental score. Adventure's original soundtrack is an iconic part of the series. Sadly, the original composer, Takanori Arisawa, died in 2005. It seems unlikely that a new composer will be able to use Arisawa's songs, so we are probably looking at a brand new original soundtrack for tri.
8. The Year
Digimon Adventure tri. will take place 3 years after Digimon Adventure 02, which took place in 2002. Assuming they don't update the timeline, this means that the year is probably 2005.
The Chosen Children's school years are now:
Takeru and Hikari: 2nd Year of Middle School (8th grade)
Mimi and Koushirou: 1st Year of High School (10th grade)
Taichi, Yamato, and Sora: 2nd Year of High School (11th grade)
Jou: 3rd Year of High School (12th grade) - unlike what many people are saying, Jou is not a university student yet. His school uniform is different from the others because he most likely goes to a private school (like he did in 02).
According to the teaser, the story should start in the summer. In Japan, summer lasts from May to August. However, since the official key visual shows the characters wearing their school uniforms, we can assume that the story beings before the summer holidays, so probably somewhere between May and July 2005. This is also supported by Taichi's confirmed age — canonically, he is 16 on April 1st, 2005 (at the start of his 2nd year of High School) but apparently he has already turned 17 at the beginning of tri.
9. Daisuke, Miyako, Iori, and Ken
If and when the 02 protagonists appear, they will probably be reduced to background characters or even brief cameos. Athough 02 is not being retconned, the focus of Digimon Adventure tri. is on the original 8 chosen children. This explains why there have been zero mentions of Daisuke, Miyako, Iori, and Ken until now — and why it's unlikely that we will see any promotional materials of them.
Lots of people have questioned how tri is going to explain the absence of Daisuke & co without retconning 02. It's actually quite easy — they will simply come up with some plot point to explain why are no longer useful for the story, like they did to Taichi and the others in 02. My guess is that now that there are numerous Chosen Children around the world, they will portray the 8 original chosen as "special" in some way.
10. Digivices
In 02, Takeru and Hikari's digivices were upgraded to a D-3, which means that the 8 protagonists of tri have different digivice models among them. How will the series handle this situation? There are several possibilities:
Everyone's digivice stays the same (Takeru and Hikari will keep their D-3);
Taichi and the others' digivices are upgraded to D-3;
Takeru and Hikari's D-3 will revert back to their original digivices;
Everyone gets a brand new digivice.
I find the final scenario to be the most likely. First of all, every Digimon series ever made had its own unique digivice/iten. Obviously, a new digivice means more toys sold and consequently more money for Bandai (the new design might be similar to the original, if they want to appeal to Adventure nostalgia). On the other hand, a new digivice might be important for the plot, by introducing different properties and even new evolutions.
11. The Epilogue
Although the 02 Epilogue is unpopular among many Western Digimon fans, it appears that Digimon Adventure tri. will not only keep it canon but also make it a fundamental part of the story. This makes it unlikely that some aspects of it will be retconed, but it also doesn't mean that tri. will be a slave to the Epilogue or constantly refer to the distant future any more than Adventure or 02 did. The epilogue takes place in 2027, 22 years after tri. — that's a long time, enough to change pretty much every situation imaginable. There's virtually nothing they can do that will directly render the Epilogue uncanonical, apart from killing off a character (which, let's face it, was probably never going to happen in the first place).
My thoughts on how they might handle some of the implications of the Epilogue:
"Everyone has a digimon partner": This is true in 2027, but it doesn't mean that it happened at once. It seems clear from the series, the 4th Digimon Adventure film, and post-02 Drama CDs that it was a gradual process that took several years and was by no means completed by 2005. As we have seen, tri. is going to explore how this happened and the difficulties everyone faced to get to that point.
Future careers: The characters are middle and high school students. This means that while we might get some glimpses of why they chose their epilogue jobs, this doesn't mean that everyone has decided their future professions by 2005. For example, it's quite possible that Yamato is still pursuing a music career at this point in his life.
Relationships: Just because the characters ended up/did not end up together in the Epilogue, this doesn't mean that all romantic relationships are settled in tri. It's quite possible that they'll show Yamato and Sora break up (and getting back together), or have Takeru and Hikari date (and later break up) — this could actually make for interesting plot elements and a source of character development. That being said, it is very unlikely that they would retcon Sorato. For one, it would turn Sora and Yamato's future children a plot hole. Furthermore, not only was the relationship between Yamato and Sora treated as a fait accompli in post-02 stories (the 4th movie and the Drama CD Michi e no Armor Shinka), but it was conceived as an important conclusion to those two character's storylines. Hopefully we can avoid the tiring and pointless shipping wars in tri.
12. Ultimate levels for everyone not named Taichi or Yamato
Those leaked images probably mean that this is going to happen in tri., especially since those Ultimates were also featured in last year's PSP game (though of course, this pics could be a dream sequence for all that we know). The real question is wether we will get other evolutions, like the potential "triangle/triple evolution". The number and scale of evolutions will probably depend on the number of episodes.
13. Parallel worlds
It would be very interesting to see the characters visit the parallel worlds that are briefly seen and mentioned in 02, such as the infamous Dark World visited by Hikari and Takeru in The Call of Dagomon (Episode 2.13). Again, this would depend on the length and tone of Digimon Adventure tri. A slice of life 13 episode series would probably not have a lot of room to explore this.
14. New characters
This theory seems to be very popular online. Indeed, both Adventure and 02 included a new chosen child who joined the team later in the story (Hikari and Ken). Could we see a repetition of this pattern in Digimon Adventure tri.?
Some people have also pointed out that a new character would be needed if they wanted to divide the group into "triangles". Obviously, the current series has 8 protagonists, and 8 isn't a multiple of 3. Introducing a 9th character would allow for 3 groups of 3 and settle this problem nicely.
However, I don't completely agree with this theory. To start with, you can still have "triple fusions" without introducing new characters. For example, Taichi and Yamato's partners already fused in previous stories. You could take the other six characters and still have 2 different triple fusions, for example SoraxMimixHikari and KoushirouxJouxTakeru. They could also introduce a system where anyone could jogress with anyone, depending on what was necessary at a particular point. So in one episode you could have TaichixYamatoxSora, on the other TaichixKoushirouxMimi, and so on. On the other hand, if they want the original Adventure characters to shine (to the point where they are willing to push the former protagonists to the side) I don't think it would be very logical to introduce a new character who will steal a lot of precious screentime from them. It seems like a waste to spend time developing a new character and exploring how she adapts to such a tight-knit group, especially if that means less minutes with the characters people actually want to see. This sounds even more unlikely if tri. is only 13 or 26 episodes long. But who knows?
However, if they do introduce a new character, I hope it will be a girl in order to correct the gender imbalance in the Adventure team. If you count all the protagonists, that's 8 boys and 4 girls.