When a cat loses its hearing does it stop purring too?

No, a cat's ability to purr is not directly related to its hearing. Purring is a muscle function controlled by the larynx, while hearing is a function of the ears.

So, even if a cat loses its hearing, it can still purr.

Your cat seems to be sleeping a lot and nose running plus not eating much is this start of cold its your first you are new things with cats?
How long do you have to wait apply a different flea medicine on my cats and dogs the one I was using seem be working anymore?