Can I use my TurboTax Premier to file a TurboTax Deluxe return? I don't care about the price difference as I already purchased the box from Costco.

Yes, you can file any income tax return except for a self-employed return. 

Thank you for choosing TurboTax.

How come it says that I have 12 returns available on my account, but when I apply the exact same code on my account at checkout, it doesn't work? I confirmed multiple times it's the exact same code within the exact same account.

You only need to use your TurboTax Online code once on the activation page. Using the code again will just give the error message you see.