Ok first Welcome to the world we Call the Matrix Online.
Second.... the servers, there are 3 and are available when you create a character.
So when you launch the client you enter your password/username then it sees if you paid ur sub like a good boy. Then shows you the latest update notes. You hit continue and it brings you to the list of your characters and servers they are on. The serve name will be on the left. IF you havent made a character then you will just have the 3 servers and under character it will say ----. Your allowed 3 per server. Syntax/Recursion are regular servers where pvp/rp/pve is all up to you. Vector-Hostile is well perma hostile. Where anyone can jump you after lvl 16.
Third... your handle as in Forums handle? Yes there is a way to get it changed. You have to submit a request to be approved. Not sure how exactly as I have never done it. If you mean in-game handle. Just delete and redo.