Moving equipment with requirements
Yes. As you state it, the requirements are there to "play the card". Equipping from another minion is not playing the card (you don't pay the cost a second time for instance).
Snodig wrote: Can a vampire A equip something currently attached to vampire B if vampire A doesn’t meet the requirements to play that equipment?
Moving retainers is more complicated, since there is no standard action to do that (you would need an Heidelberg Castle for instance).
Ratadin wrote: I would like to remind that, even though you can, for instance, move a Erebu's Mask from a Harbringer of the Skull to, for instance, a Malkavian, this wouldn't benefit from the +1 Stealth as the mask specify "This Harbringer of the Skull...", and the malkavian isn't a Harbringer of the Skull. Meanwhile, you coould move a Revenant from a Tzimisce to the same malkavian, and the malkavian would then gain +1 intercept, as the card specifies "The minion with this retainer", and the malkavian is a minion.