I haven't tried that in multiplayer. Do you mean game breaking as in overpowered, or actually crashing the game?
If it's the former, I think the slow movement and projectile speed is a reasonable effect if confined to a radius. Also, I'm sure some combination of decreased gravity and decreased jump height could make aerial movement seem slow-mo as well.
Pretty sure you're right, but I wonder if the Globals can be changed in the same way you switch to your custom character. If you could swap to your own modified Globals, I think it could change a lot. I'm pretty sure that's where simple skills like "Jump" are set. But even then, I don't know if you could modify the jump skill to allow double jumps (while also having the default jump if the skill is inactive).
I think there might be an IsFalling attribute that you could use to determine if your player is jumping. The enemy below you thing is probably not possible or more trouble than it's worth. The rest could be done I believe.
Side-note: Melee override skills are possible right? I don't remember what it looks like where you enter the character's melee animations, but can you place multiple anims with parameters (like with weapons)?
I wonder if TexMod works in BL1. I know it does in BL2. If so, you could change the skill icons.
But yeah overall making a character is a lot of work.