If I remove a card from my opponents deck, it goes to their RFG zone?

If I play that card, does it go to the owner's KO pile or remain RFG?

It goes to its owner's KO'd pile.

Just to be clear, how does "playing" the card work with equipment, ongoing PT and locations?

Reading over rule 505, it would seem like you would be able to recruit an equipment you removed with Master Thief, and I would imagine only non-ongoing PTs (or the non-ongoing part of an ongoing PT) would work, but what about a one time location like Brother I or the Great Refuge? Would "playing" the card with Thief trigger that effect?

thats why you dont remove anything except equipment, characters or plot twist :O