There are six wizard slots for each account. If you have six already you will have to delete one. I'm pretty sure the membership works for all accounts too.
No, the old one is not deleted. You can have up to six characters, and you must manually delete them. Membership and Area Purchases (with crowns) are for the entire account, not just one wizard.
Your new character will get membership, only if your old had membership, and it is on the same account. Plus, of course your old one will not be deleted