Tried that. Your colleagues, and some managers, will immediately see you as a threat (how dare you have something to show when we don't) and will start treating you as a personal enemy. Sabotaging every thing you are trying to do, trying to blame you for every failure, and overloading you with completely useless work.
Nope, fish rots from the head. If everyone around you is useless, there are good reasons for it, and best you can do is find another place where these reasons won't apply.
Nah, I'm a tough and a cynical dude. I used my time at BigCo to practice the skill sets I needed, saved some money and jumped ship to running my own business. It's hard, but it's infinitely more rewarding than the rat race.
Nope, fish rots from the head. If everyone around you is useless, there are good reasons for it, and best you can do is find another place where these reasons won't apply.