For unquilting, I use a box knife blade. I pull the sandwich apart as much as I can and just touch the blade to the threads, and they cut like butter. This does leave bits of threads, so I run a cheap emery board across the fabric and it picks the threads right up. No, I have never cut the backing or batting, and the blade doesn't get anywhere close to the top.
For unsewing, I picked up Ricky Tims' frogging technique. He takes the piece in question, snips the first 4-5 threads, then with hands on both sides of the patch or piece in question, he rips. Literally. Just like ripping yardage. He yanks the seam apart. I wouldn't do this on anything bias, though.