I can't speak to the rest. However, #3: from what I know, ctrl-g turns the Screen Icons off and on and has nothing to do with hiding.
On #2, from what I have heard, if you drink the potion, you are evil for the entire fight, not just until you get defeated. For your team to win and the battle to be won, the Nefarious 5 AND you must be defeated.
While wearing the Nefarious 6th badge that gives the glowing eyes effect, your facial accessory will be hidden, so as not to steal the spotlight from your cool glowy eyes.
With all due respect here though, though I can definitely understand the reason as to why this is like it is, I really do wish that there'd be an option for this. For example, with the Black Rain Shades and the Nefarious 6th badge both equipped, I can be like the Terminator of sorts and say "I'll be back!", and I'm sure that other people would love to have different combinations of effects with the items and the red, glowing evil eyes as well, so please at least consider making this an option to either have accessories hidden or not hidden while having this badge equipped please, so there's that at least.