This then brings up the issue of injuries/illness that you can't heal from naturally, like amputation or cancer. Will granny's power work on those?
It'll be very liberal. Izuku's leg was twisted after he smashed the big robot, but Recovery Girl's healing actually twisted it back into place without requiring manipulation. If we take her explanation literally, his leg should have healed in a twisted position, since normal healing doesn't shift bones back into anatomically correct positions.

If you suffered full thickness burns, accelerated healing would just mean instant scar tissue, since you've lost the basal layer for generating proper skin cells.

If stamina was just energy, then as Shinta said, a dextrose infusion should suffice, maybe along with some insulin, parental nutrition and what have you.

But that's no fun. Better to have her explanations interpreted loosely so there's a story to tell.