I've done a lot of research into coast live oaks, which looks like what you have.
1. Leave the branches if you want to thicken the trunk. You can cut it off at any time. I think it's in a great place already, so I'd say you should leave it until the trunk is as thick as you want.
2. The roots are very sensitive on this species, so I think
@just.wing.it is right and you should cover the roots. If you want exposed roots, do it slowly over time. Also, the best time to do repot or do anything with the roots is from late fall to early spring, when the tree is in sleep mode.
Here's a great video regarding how to deal with coast live oaks. This guy has been working on these for many years, so I'd listen to what he has to say.