Click on the commander when you're in the lobby - which is right next to your name, Just like choosing a color.
To the best of my knowledge, that's slightly incorrect. As I understand it, different commanders will come with different abilities/weapons. Of course, this isn't implemented at all yet. All commanders currently behave and perform identically.
No. Uber has stated that all Commanders will be exactly the same – except they'll just look different.
The plan was for commanders to have slightly different abilities that won't have a major effect on which one is stronger. After all the hate Mavor said he may remove all abilities entirely. Only time will tell.
You can put spinners and hydrolics on them. I hear Uber is in the process of getting spoilers and body kits too.