Eep. Yeah definitely get those mites taken care of. There is nothing worse than getting eaten by mites... and if it will bite a rat it will bite you!
Handfeeding is fine, and a wonderful tool to bond with your rats, but for all the years I've kept rats, anytime I started routinely handfeeding them through the bars they would develop this grabby bite reflex. Now I just handfeed them by opening their cage or do it while they are out.
Good luck with your new little guys. They will become a new addiction for sure!