If your cat is throwing up hairballs often, consider using petromalt, laxatone, or another hairball remedy. Repeatedly thowing up can be dangerous to a cat. This is not something their ancestors did in the wild, as their diet included enough (fiber?) to keep the ingested fur going right through their systems. My vet said thowing up constantly can result in a torn diaphragm(?) which is fatal. I give petromalt once a week. It noticeably reduced the amount of hairballs.

As for the shedding, I too just consider it part of being a cat - a purring machine inside a fur factory. The factory just keeps working producing more and more.