"I'm also a little suspicious of the "inconclusive" background check. Not sure what that means."
I think item #9 in the 10-point code deals with that. When a NICS background check is run there are three possible results
roceed, deny, or delay (the firearm transaction). A delay response gives the NICS agents (nominally FBI) three working days to make a determination whether the transfer should take place. If after three days, the transfer is allowed (inclusive result not withstanding). NICS will sometimes call back when they DO make a conclusive decision, even months after the transfer was made if it is to 'proceed'.
I had one callback on one of those 'inclusive' ones after the transfer was made to say it was a denied result. Rest assured they wanted all the personal data the applicant had written on the 4473 form and I assume he was contacted shortly.
Jim