Does a passport work as proper i.d ? Also, can i recieve the proper background check at the store?

A Passport does work as official ID.

Unfortunately we can only accept State issued ID because we need legal verification of the purchasers address. We provide background checks for in-store purchases at no charge and for a small fee for person-to-person or FFL transfers

Not sure about a passport, but all gun sales through an FFL require paperwork, a NICS check, and a waiting period.