Can the devil and false prophets perform miracles, and what are the limits of their power?

Yes, we call it preternatural: they can take something already created and conform it to their wishes, so that when we see it, it looks like something it was not before. They cannot create anything; they can only use what is already there and distort it. In Moses' time the magicians made their staffs appear as serpents to challenge Moses; the witch of Endor made it appear she was bringing Samuel up from the dead to speak to Saul. So yes, false prophets can perform miracles, but usually of the deceptive, illusory variety. They do not truly raise people from the dead, because that is creation, though they may animate a body with their spirits so that it looks like a resurrection. When the Bible speaks of genuine divine miracles, these are things the devil cannot imitate on the same level: actually raising the dead, as Peter and Paul did, putting limbs back on people, curing the blind so they can see. Those get their status as genuine miracles because of the tremendous alteration of nature that has taken place, and you do not find the devil doing them.