My understanding of the RS2K process, is if a provider is approved to join RS2K, she provides the name,contact number and city the hobbiest is
from, she will be told that the hobbiest has been verified and is approved , unless of course ther has been negative feedback from providers using RS2K conerning their saftey and the hobbiest
Recommend you contact RS2K Cathy directly to get answers to your questions

Good luck

Can a provider call and ask RS2K your history?  Does RS2k have that sort of information, and more importantly, would they tell them that sort of thing?

Easier question - can a provider access your history of other providers through RS2K?

They do not keep info on who asks about you, all they keep is a small amount of info to verify you and then if any provider had a problem with you it is also noted.  So if you short, abuse, rob, attempt BBFS, NCNS then that is assured to be noted but they do not note who you have or have not seen.