I appreciate the replies. I will discuss them with a friend of mine to see what she thinks. In the meantime, I would like to share some of my thoughts.
1. Re: the nature and EV spread on Politoed.
Of course, Politoed exists solely for the rain. But the reason I invested in Def is because he has decent SpD, and the reason I invested in SpA is just in case I need to use him as an almost last resort to deal some damage.
2. Re: Vaporeon.
I think Vaporeon has fantastic stall capabilities. It is able to withstand a solar beam from even Mega Charizard Y in the sun. Also, toxic annoys everything that is not Steel or that does not have Magic Bounce/Magic Guard. Wish provides enormous support for either Vaporeon or its teammates, especially helping Dragonite keep Multiscale intact.
3. Re: Ferrothorn.
I was able to breed a Relaxed nature Ferrothorn with perfect IVs in HP, Atk, Def, and SpD and a 0 IV in Spe, thus providing a solid base for getting as much out of Gyro Ball as possible. I am still unsure about the EV distribution. I think 252 HP is necessary, and I like the idea of investing 252 in SpD in order to withstand Focus Blast, Aura Sphere, and special Fire attacks, especially in the rain. I put the remaining 4 EVs in Def, which, combined with his naturally high Def and the boost in Def he will receive from the Relaxed nature, should enable him to survive physical hits pretty well, whether Fighting, Fire, or Ground. That is the reason I also put Iron Barbs and a Rocky Helmet on him: to punish physical attackers and make them think twice about dishing out such hits.
I am also unsure about Leech Seed. It is a standard move for Ferrothorn sets and provides good recovery, but I also worry about opponents switching out with it, and it is useless against Grass types. Is that still the best move, or is there another move I could consider?
4. Re: Volcarona.
I will consider the Passho Berry. But I worry more about Ground and Rock attacks than Water attacks, to be truthful, because I can always switch into Vaporeon or Dragonite to absorb the Water attacks. Is there a Berry that minimizes damage from Ground or Rock attacks? I haven't done the research on that so that's why I'm asking.
5. Re: Dragonite.
Everyone seems to consider him broken, even with Multiscale. And I know that there are challenges to using him, but I don't believe he's as broken as people believe. As for switching him out with Mega Ampharos or Mega Manectric, doesn't that just open me to a gigantic weakness to Garchomp, Lucario, etc? Aren't they far more common threats than, say, Thundurus?
Two more things. I do generally favor Surf over Hydro Pump because of its greater accuracy and because of its higher number of Power Points. Especially with something as frail as Greninja, sometimes accuracy means more than power.
Finally, to the last person who replied to my post - MoxieInfinite - while I appreciate the time you took to reply and give your opinion on the subject, (1) please stop using bizarre abbreviations that only the initiated and elite understand. I don't have the time or desire to go to some Pokemon dictionary to look up all the abbreviations and jargon. (2) I don't use Latias/Latios (if that's indeed what "Lati" refers to), just like I don't use any other legendary Pokemon, because (a) you cannot get a perfect IV one without hacking, and hacking is for losers, and (b) because they are a pain to try to transfer over from previous generations.
In any event, thanks everyone for their opinions. I will consult with my friend and share my ideas with her as well as the stuff you all brought up and I will see what she says. I'm sure you guys have good points in there, and quite likely some of my thoughts, though logical to me, may not be as useful for or accurate to the metagame as I would like to think. Thanks!
Wouldn't it be a better idea to use Modest with 172 HP/252 SAtk/84 Spe on Politoed? This lets it outspeed stuff up to 0 Speed Venusaur and Mandibuzz and gives it better all-round bulk as opposed to just 252 Defense EVs.
Rain stall is ineffective this generation because of the 5/8-turn duration of Drizzle. Vaporeon was severely hurt by this change, rendering its Hydration-stalling days over. These days, rain is all about offense, using support Pokemon only when necessary. Also, Charizard Y takes pitiful damage from Scald in sunlight, giving it more than enough time to take Vaporeon out with Solar Beam:
0 SpA Vaporeon Scald vs. 0 HP / 0 SpD Mega Charizard Y in Sun: 84-98 (28.2 - 32.9%) -- guaranteed 4HKO
252 HP/88 Def/168 SDef is the optimal spread for Relaxed Ferrothorn. This gives it more Defense to take on physical attackers, while still giving it enough special bulk to live resisted special attacks. Leech Seed also deters opponents from using Ferrothorn as setup bait and Ferrothorn can't do much to Grass Pokemon anyways.
Greninja isn't the strongest Pokemon out there, which is why Hydro Pump is preferred over Surf simply because of the higher power and Greninja needs all the power it can get.
Remember that Mega Ampharos outspeeds plenty of stuff after an Agility, while Mega Manectric outspeeds Garchomp outright and weakens it on the switch with Intimidate (neither should be brought in directly, though). Both have their own ways of dealing with Garchomp in Dragon Pulse and Hidden Power (Ice) respectively:
252 SpA Mega Manectric Hidden Power Ice vs. 4 HP / 0 SpD Garchomp: 312-368 (87.1 - 102.7%) -- 18.8% chance to OHKO (Garchomp needs to be weakened for a better chance of HP Ice to get the KO)
252+ SpA Mold Breaker Mega Ampharos Dragon Pulse vs. 4 HP / 0 SpD Garchomp: 420-494 (117.3 - 137.9%) -- guaranteed OHKO
The trick is to bring either of them on something they scare out, then act accordingly if Garchomp is brought in.
Volcarona isn't weak to Ground; it's only weak to Water, Rock and Flying. In case you're wondering, Charti Berry is the Rock-weakening berry; Shuca Berry is the Ground-weakening berry. Coba Berry (which weakens Flying moves) could be used if you're afraid of Mega Pinsir's Quick Attack.