i'm not sure on the skull, but there is only one claw there, the other 2 are teeth of some sort. the last pic shows the 2 that are teeth. the claw looks like it may have come from some raptor, like a hawk, or maybe even a small bobcat, its hard to tell from the pic. how big was the burm you got these out of?

the skull is defiantly not a rat, rodents are all molars and incisors. could it be a juvenile Nile monitor?