Yes, the code you first received was just for early access, you'll get another code with the physical game. I assume this is the same as if you bought the digital download, you'll get another code emailed to you/on your account on Tuesday. The early access code will still work until the 29th I believe, so if it takes you a few days to get your copy, you won't have to worry.

As for not putting billing info in, I'm pretty sure it's mandatory, at least it is with most (if not all) other MMORPG's I've played. You won't get charged until your free time is up (15 days for 1.0 users, 30 days for new users)