I am wondering....(many questions here)

[Caliber70]

what affects pokemon relationships? what is the formula and factors?
who has done the testing?

# TIME? do they like you more depending on how long they have been with you or away (inside box1?) ?
# of VICTORIES? is it from winning battles? or just participating but not necessarily winning battles?
# of FAINTS/LOSSES? is it tied to fainting?
o_O or is it a combination, a K/D ratio?
# of LVLs GAINED? or is it tied to only number of levels gained?

does using selfdestruct or explosion change how they like you negatively?

if you are their original trainer, and you only have the badge that commands up to level 30, do they stop obeying at a certain point?

if you are the original trainer and you trade your monsters away, and trade it back, does it still know you? is that monster's relationship still the same as before trading it?

i know traded ones stop obeying depending on your badges, but if your traded ones have maxed 'like' for you, do they still stop obeying past your badge level? like if i trade a chimchar at level 1 and have the badge for commanding level 50, and train infernape past 50, does all the 'like' it has for me just disappear and not matter?

i would imagine with hacking tools these things can be determined right?

 

[Sopheria]

Friendship is summarized in this Bulbapedia article.

what affects pokemon relationships? what is the formula and factors?
who has done the testing?

# TIME? do they like you more depending on how long they have been with you or away (inside box1?) ?

Not time, but the number of steps you walk while the Pokemon is in your party. After a certain number of steps (the exact number varies from generation to generation but in the current generation, it's 128), your friendship with all the Pokemon in your party increases.

# of VICTORIES? is it from winning battles? or just participating but not necessarily winning battles?

Nope. Winning battles doesn't affect friendship.

# of FAINTS/LOSSES? is it tied to fainting?

Fainting results in a decrease in friendship.

# of LVLs GAINED?

Each time a Pokemon levels up, its friendship level increases.

does using selfdestruct or explosion change how they like you negatively?

Yes, there will be a decrease in friendship due to them having fainted.

if you are their original trainer, and you only have the badge that commands up to level 30, do they stop obeying at a certain point?

This one I'm actually not sure about. I feel like it's happened to me before, but I'm not 100% certain I'm remembering correctly...

if you are the original trainer and you trade your monsters away, and trade it back, does it still know you? is that monster's relationship still the same as before trading it?

Trading resets friendship, so even if you trade it back, its friendship has been reset.

i know traded ones stop obeying depending on your badges, but if your traded ones have maxed 'like' for you, do they still stop obeying past your badge level? like if i trade a chimchar at level 1 and have the badge for commanding level 50, and train infernape past 50, does all the 'like' it has for me just disappear and not matter?

Friendship isn't affected by obedience, at least to my knowledge, though maybe someone can correct me if I'm wrong :x

i would imagine with hacking tools these things can be determined right?

They have been ^^

 

[acatfrommars]

I don't think that obedience and happiness really correlate. It depends on the game, but certain items such as Vitamins can help build up a Pokemon's happiness among other stats. Also, in the newer games there is Pokmeon-Amie which can help with happiness I believe.

 

[VisualJae]

Badges and obedience only apply to Pokemon you didn't obtain yourself (i.e. any Pokemon that doesn't have your original trainer ID).

The obedience mechanic is only in the game to prevent new players (or newly started games) from twinking, a common tactic used for any RPG game. It is also designed to incentivize obtaining your own Pokemon in your own game. For Pokemon you didn't originally own, it doesn't matter what the Pokemon's friendship or affection levels are (side note: friendship and affection are completely different mechanics). You don't have the qualifying badge, the Pokemon won't obey.

Trading resets friendship, so even if you trade it back, its friendship has been reset.

Actually, in Generation VI, if you trade a Pokemon and it gets traded back to you (doesn't matter if it's right away or there have been a dozen other trainers in between), the friendship value is restored to the value before being traded the first time.

 

[Drayton]

Fainted lots of time or using a move that induce suicide (self-destruct, memento or explosion) could lower your pokemon's happiness (friendship)

obedience is different than happiness, it just prevent new players from progressing so fast and easy from getting a traded pokemon that is insufficient badge requirement.

I'm not sure about obedience + badge theory, but maybe if pokemon you caught have exceeded the badge level requirement let's say have a 1st gym and say up to 30, then it reaches level 31 it could whether obey you or disobey you I think it would disobey since it's only saying up to 30 and not more than 30, but I could be wrong.

 

[VisualJae]

I'm not sure about obedience + badge theory, but maybe if pokemon you caught have exceeded the badge level requirement let's say have a 1st gym and say up to 30, then it reaches level 31 it could whether obey you or disobey you I think it would disobey since it's only saying up to 30 and not more than 30, but I could be wrong.

It's not a theory, it's a known mechanic. It only applies to Pokemon you don't obtain in your own game (most commonly through trades).

You can take the time to grind your level 5 starter Squirtle on Route 1 until it's a level 100 Blastoise and it'll still obey you even if you didn't reach Viridian City yet.

You can go to Viridian City and have your friend trade over a level 40 Charizard and that Pokemon won't obey you until you get the Rainbow Badge.