These questions were answered already, I I answered to 1) and 3) and someone else posted info on 2).
1) NC has nothing to do with FP, they are separate checks, NC initiates soon after filing I-485 (one day to one month) and FP notice is mailed when they think you may be approved within next 15 months, if this not happens then they mail one more FP notice like happened to me.
My NC was initiated one month after I-485 receiving (oct 2003), 1st FP done one year later (oct 2005), 2nd FP done after 1st expired (Feb 2006).
2) 'security check' is I think 3 checks, one is name/DOB (date of birth) and this one takes longest time, one more is IBIS (not sure on spelling) and takes short time (maybe minutes) but expires soon and has to be retaken when close to approval, and I do not remember what is the 3rd one, I think also takes short time. Search this thread for more info.
3) earlier FBI replied to faxes and e-mails, now they stopped doing it and only way you can find out is to ask your senator/congressman to contact FBI on your NC status. I tried infopass, you may be lucky and get this info if the officer will be nice. For my last infopass visit the officer refused giving me any info.
you may also try Natl customer Serv Center but they may just give you status (pending) but not the date when it is initiated.