I don't really understand what you're talking about for the first question... Sometimes they need to verify membership eligibility for military members by making sure they were actually in the military, DOD, etc. However, it's a bit easier when you're a family member: in your case I assume you just entered your dad's access number or something, which can be immediately verified internally.
As per your access number, you should receive a card with your access number on it within a week. If you're looking to access NFOAA (online account access) to perform transactions online, you'll need your access number for that. If you haven't received your access number yet in the mail, you can still enroll in NFOAA online. Just go to http://nfcu.org/accountaccess/index.html and click on "Enroll Now". Fill out the required information and when you have to enter your access number just click on "Find Your Access Number" and enter your information and it'll pull it up for you.
You can still do transactions over the phone or at a branch with your account number, but you'll need to provide some form of ID. In the meantime, be sure to mail in your signature card.
