Holy wall of text.
Just wanted to weigh in on a few things.
RE: The whole idea - I like it. I've always felt that the vanilla enchants were a little underwhelming.
RE: Knockback - Not a bad idea, kinda similar to the right click of mDiyo's Rapiers though, but WHO CARES! (Just please make it intelligent enough so that the player doesn't fall off a cliff.)
RE: Fire Aspect - Not really all too sure when I stand on this suggestion. On the one hand, the name "Fire Aspect" implies that you imbuing the weapon with aspect of fire (I hate making circular references), but on the other, the blade becomes attributed to everything fire-related so it would stand to "reason" that the sword would be able to absorb incoming fire. Heck, if you really want to, hit the mob and set it on fire, block and the sword will "absorb" the incoming fire and give you maybe a 2-second strength buff to symbolize the short-lived increase of energy within the sword.
RE: Punch - Like you, I never really understood why you need an entirely new enchant for knockback for bows, and I've never quite made the connection as to why the bow needs to be enchanted when it's the arrows that are actually striking the mob. As for giving the bow's left-click the Punch/Knockback, I like it because, to me, it's a throwback (see what I did there?) to the medieval times (or the Chivalry game, if you play it) where the archers would strike their opponents to force them back in the opponent is up in their face.
RE: Feather Falling - PLEASE GOD PLEASE! This would actually make the enchant worth something if you're playing with mods.
RE: Thorns - Ehh... Never really used it, so I wouldn't know.
RE: Unbreaking - I'd rather keep it as-is. Unbreaking implies that the item won't break under normal circumstances, everything will break at
some point, and if this is the case, then you're already, technically, extending the durability while keeping the same numbers; just more hits can be taken per durability point.
RE: Removing Enchants: Go right ahead with this one. Although, I'd personally keep Smite what with the Zombie horde reinforcements feature of the recent versions of Minecraft.
RE: Enchanting "Illegal" Items - Ehhh... Sure. Why not?
Looking back at this, I shouldn't have put the "Holy wall of text" line in, I'm just as bad.