1) Haven't quite gotten to that point yet, but from the sound of it it's extremely silly. Should be altered in some way.
2) Seems to be the easy fix is to have invisibility turn off before you pick up items. As for using it to avoid fights, that's the player's choice. Consequence free stealing isn't balanced, but avoiding fights comes with the penalty of no experience and loot rewards.
3) I agree that dialogue traits are often incredibly unintuitive, and would not be adverse to your solution.
4) Lockpicking and dirty deeds need a buff, period. Lowering lockpick requirements might be a step in the right direction.
