I mean, theoretically you can but I would strongly advise against it. The reason being that the expertise that you get from the PvP gear does absolutely nothing for you in PvE. It's strictly player damage/healing/damage reduction.

Yeah, as of right now there are no options for HM Ops. The reason for that is most likely because there is no "gear check" for the group finder at the moment, and you don't want some new 50 in you're group with crap gear for a HM Ops. Things would go really wrong, really quick.