[cypher]

The licking & nibbling sound quite normal, Russians do quite often lick your fingers which is really rather sweet! Nibbling is often just confusing fingers with food, if she's not actually biting then it's something she probably will grow out of with time.
Russian hams nails do grow fast, unfortunately putting things like stones in the cage won't help much, the sand bath can help a little & some natural rough surfaces in the cage like wood, stone tiles like granite or just an ordinary kitchen wall tile turned upside down (they are rough on the back) will also help but most do need regular trimming.
Some hams do get a bit stressed especially if the person doing it isn't that experienced in holding hams while trimming nails so it's often best to just do a few at a time.

I would make sure the cats can't get into the room where she is, it will be very stressful for her to have cats around her & jumping on her cage definitely shouldn't be allowed.