Does this bolt to the factory cat, or do I need to replace that too?

This is a catback system, so it connects directly to your stock catalytic converter. You're only replacing the pipe from the cat back.

Will I need clamps, gaskets, or other hardware to install this?

The system assembly is included. Check that the factory mounting hangers are in good shape before you install — if any are bent or missing, you'll want to replace those first.

Does stainless steel really not rust?

Stainless resists rust far better than mild steel, especially in wet climates or if you drive through salt. You'll still get some surface discoloration over time, but no structural rot like you'd see on a steel exhaust.