A paid collection is no better for scoring than an upaid one - only boost will be with a PFD.
GW the auto loan company - can't hurt if the account is current or PIF.
Truthfully, I would attempt the PFD (DV first though if past SOL) before trying for a card. Might take you 30-60 days to ether get it off via a DV or a PFD... and probably better choices of cards as a result.