I've never seen any evidence that it's not okay to refreeze, but I personally don't. Better to be safe than sorry. On the few occasions that I have, none of the snakes would take them the second time around.

As for disposing rodents... I'm not sure there's much else to do besides throw it in the trash. Or you could buy a blood python, they work great as rodent disposals. I haven't had to throw away a single rodent in nine months.