One - Okay, WITHOUT bonuses at all, the Master level frenzy spell, Mayhem, will effect enemies up to level 25. The following perks add to that level limit in the following amounts:
Animage (+8 on ANIMALS)
Kindred Mage (+10 on HUMANS
Rage (+12 for frenzy spells)
So with those perks, the level cap increases on Mayhem from 25 to 45 on animals and 47 on humans.
Illusion Dual-Casting doesn't work for Master level spells since they require both hands to cast, but it does for single hand spells, so lemme do the math again for the best single hand frenzy spell, Frenzy.
At base level, frenzy effects enemies up to level 14. Dual casting APPROXIMATELY doubles this number (the doubling happens before perks are applied), this brings it up to 24, 12 gets added from rage, making it 36, which makes 44 or 46 depending on types of enemies.
Something of note, Animage unlocks at 20 illusion, Kindred Mage at 40, and rage at 70, so you wouldn't be gaining all the perk bonuses until at least 70 illusion.
Two - Your illusion perks won't effect your potions. As for highest level for a potion, that's a hard number to pin specifics on, as there are a lot of factors that can be manipulated as well as a general vagueness of information about the potion creation process.
THAT SAID, the fact that you can get the level cap up to the high 40s with just perks alone means that you won't need the best possible potions to make it that your spells can effect any non-immune enemy in the game.
Three - Dragons are always immune to illusion regardless of what you do. Undead(Dragrs, Vampires, etc), Daedra, and mechanical constructs (Steam Centurions, Worker Spiders, etc) are all immune until you take the Master of the Mind perk at 90 illusion.