Creating second Developer Account
Is it better to create new Apple ID for my developer account, or is it ok to use my existing one?


I would recommend creating a new one. Apple doesn't seem to care either way, but it's usually a good idea to separate the two accounts.


  And what are the rules regarding names (like can I use nickname or I have to use my real one)?


You have to use your real name. This is for identification and since the agreement is legally binding, I wouldn't risk it (plus, do you really want DenverCoder9 to show up on your banking records?).