Can someone find out if you have paid to have a background search done
on them?  How do you find out who has searched your background other
than employers or legitimate creditors?

To answer your question yes and no. A  back ground check consists of
several things credit history, driving statues, past employment
etc.... the problem is such things as credit checks can be traced back
to who asked for the check but other things such as past employment,
driving statues cant.

read this it will help you understand the system

http://www.bankrate.com/brm/news/advice/20050216a1.asp