Ok First Question: How to check if someone is logged in.
The best way I have found to do this is generate a uniqid() for a user WHEN they login. You then save this in a database and a matching on inside a cookie and each time they load a page, check to see if the cookie exists, and search database for matching one then you can compare it to the member info.
To stop duplicate usernames:
Simply Do a search query on your database when someone registers. If it exists return an error, else let them through.
An Extra note:
Keep your users data secure. Use salt+hash and you should be good. Personally I do this:
Password = User input
Salt1 = Constant
Salt2 = Constant
Salt3 = Username
Password = Salt1.Password.Salt2
Password = md5(Salt1.Password.Salt2)
Salt1 = md5(Salt1)
Salt2 = md5(Salt2)
Salt3 = md5(Username)
Password = NewSalt1.Password.NewSalt2 <-- Notice the password here is the hashed one above
Password = md5(Password) <-- Password here is direct line above
Password = Salt3.Password
Password = md5(Password) <-- now hashed with username as well.
This prevents someone using rainbow tables to work out peoples passwords if they get a hold of your database
