First off, mad props to be open to criticism via an internet forum. I actually spent the time to read everyone's critique on this forum, and I have to say I am more and more impressed with the group that is on this forum.
Anyway, much of the things have been covered. I know its unconventional, but when I first started training (going back aways now, bear with me) I was taught to hit a bag with a towel under my chin, it gets you in a good habit of keeping your chin down. But don't stop there, like many others said keep your hands up. As someone previously put, you are a 'counters' dream, I know I got a little excited watching you.
You seem to have the rest of the critique done by others. As far as dieting/exercise I would say get a jump rope, a light kettebell, and some good running shoes. I can't give you a definite answer on how long/duration/etc etc since I don't know you, nor do you know me (or care). Shadow boxing with resistance tubing is key as aforementioned.
Finally, check out some Crossfit
work outs, some you may be able to do in your gym, others you may not. But its a good full body workout, and you if you do it properly you should vomit the first few times....its a good feeling.
And finally, if you really want to lean up, I would stay away from doing isolation exercises, keep it mixed up don't focus on one-two body parts a day. Check out some of the training logs for some ideas. Good luck, keep us updated, and have fun!