In order as they are listed:
1. Balance
Weasol: I'd say definitely balanced. It's fast and powerful, but it's also frail. It could defenitely run a swords dance set that would destroy everything once it's checks are gone, but it'd kinda be taking a gamble whenever you play it, though it would definitely be worth it in the hands of a decent player.
Beegon: Undoubtedly unbalanced. Beedrill is already totally viable in OU, and beegon is just better in every way. Better bulk, faster, better typing, more powerful, etc.. Yeah, were gamefreak to actually make this thing, I would give it a solid week in OU before it was quick banned. Tops. It's just so broken, even w/ all the other powerful threats running around. I think it would be better w/ gliscor over flygon, as it gets greater far better physical bulk at the cost of a minuscule amount of special bulk and even less speed.
Tyranichomp: I'd say possibly (?) balanced, when compared w/ everything else around it. But then again, it would basically destroy literally any wall w/ garchompite. However, other than smashing opposing walls, I'd say garchompite isn't actually that good. Tyranitarite is the one that I think would be the most devastating set. 101 speed, like, are you kidding? It's like it was designed to speed creep. Just enough speed to beat the average speed tier (in OU, I guess, it would def be different here), and freaking Dragon Dance- Garchomp's dream come true. W/ that attack stat too... Gross.
Railie: I'd say this is balanced for a number of reasons, despite its impressive offensive movepool, ability, and great offensive typing. First of all, it's an Ice type, which sucks. Along w/ that, it's parent's stats (a decent indicator of its own stats, relative to the meta) are pretty underwhelming except for speed. However, Fridgespeed + stab boltbeam coverage is awesome, its main stab moves are really powerful as well, and it gets swords dance to let it sweep. Along with its trash defensive typing, it's rather frail, though not terribly so.
Charatos: I can't honestly see Y being that good, as it loses SpA and sun weakens its water stab, which is lame. X, on the other hand, I can guarantee would be solid. Its just a better Char X. Its faster, stronger, and gets TC boosted water coverage, though that's not necessarily your first choice. And it gets 101 Spe too, which is awesome for a dragon dancer. Its base form could be cool too, as it gets great stab coverage.
Aggrosaur: This thing is awesome. Imagine ferro w/ a better ability for a wall/tank, better stats all around, and recovery. That's disgusting. I don't know if there's a lot more I can say than the post already says.
2. Sets (Same order because I don't want to type out the names again)
-I'd say a swords Dance Sweeper w/ knock off, Sucker Punch, and Play Rough, just like absol usually runs, just better, is the best option. That, or an AoA set could be great and really simple too.
-due to the substantial increase in bulk, and by corollary, far lessened weakness to priority, I'd say a swords dance sweeper would be very effective. Earthquake, X-Scissor, Swords Dance, Poison jab/Dragon Claw/Knock off(/protect) would be great, with any of the coverage options working depending on the team. It also gets rocks, and could also run a lead set or it could run a hit and run set like beedrill usually does. That would be simpler, imo, but less destructive overall.
-dragon dance sweeper w/ Stone Miss / Dragon Claw / DD / EQ. Its best option would be tyranitarite, as the boosts its speed puts it at an incredible speed tier for a dancer and it's already not lacking in the power department.
- fairly certain this one doesn't need a lot of explaining. Espeed / SD / Volt Tackle / EQ. Adamant, 252 Spe / 252 Atk. Simple enough- set up and kill. However, it does get access to the uncommon spikes, paired with fridge-boosted explosion, making it a great suicide lead. However this wouldn't usually be as good as an Ekiller set.
-*copies and pastes charizard X's offensive DD set...* However, guaradosite could actually be great too, as it would do very well against stall, while retaining Zard X's offense-breaking power. Either way it's run basically the same set, just swapping out crunch over dragon claw and sub/ taunt over EQ.
- there are so many possibilities w/ this thing. Its fast enough for dragon dance (I think aggron can learn it), has an awesome support movepool, it's super bulky w/ great power... the list goes on. I can't really say what would be best, as 1, that completely depends on the archetype, and 2, who knows what all it could run. The options are awesome on this thing.
3. Checks and counters:
-I'll do this later cuz I'm bored.
4. (Question 3, pt 2):
- see question 3.