That looks like a Fukien Tea (ehretia microphylla).
They like LOTS and LOTS of light. If you search this fourm, you will find a lot of information, also u can google it.
I'm a new to bonsai myself so I can't anwer your questions with confidence. but here's what I can tell you... and someone else may come along and correct me, or provide better info.
The soil is definetly wrong, so u may want to re-pot within a month or so, but make sure you do some research on the type of bonsai "soil" u should use.
Re-potting is stressful for the tree so I don't think you want to re-pot AND cut a large branch all at once. Don't try to do everything at once to any tree, every "modification" is stressful to it, so you should give it some recovery time after each step.
And it may be better for the moss to be removed since the tree is in poorly draining soil right now.
As I said I'm new to bonsai myself, and by no means an expert, but I've owned my Fukien Tea for about a month and a half, it seems to be happy with 14 hours under flourescent light, on a humidity tray, and water misting to maintain humidity, I do not water mine often since it's also in poor-draining soil for now. I use the chopstick method to determine when it needs to be watered.
The reason I think my tree is happy is because it has constant new growth, and blooming.
Good luck!
