A skinny cat may still eat. It isn't about how big or little they are, it's about not eating over a certain period of time. And by not eating I don't mean taking a bite here or there, I mean not eating anything, period.

If you're force feeding, that is considered "eating".

You can give SQ fluids at home, but your vet needs to be the one to prescribe them and tell you the correct amount to give to your cat.