I was wondering, is it possible to create a new account? As in, can I go to my BattleNet account and just bind/create a new account out of nowhere?

Ya.

Its not like an entirely new account, just an account within your BattleNet account.

they can play at the same time.

But if you are sharing with a friend, know that it uses only one password, so your compromising the security of your account.

and you can make one with either a new wow card or you can shave time off of your account to make a new one.