Does this radiator come with a new thermostat housing or petcock?

No, the radiator assembly only. You'll need to source those separately if replacement is required for your installation.

Can I reuse my existing hoses, or do I need new ones?

Your current hoses will fit the port connections, but inspect them during install. If they show age, cracks, or hardening, swap them out — a failing hose will take down a new radiator fast.

Do I need to flush the cooling system before dropping this in?

Yes. Old coolant carries debris that clogs a fresh radiator core quickly. Drain the old system, flush with distilled water, and fill with fresh 50/50 coolant before start-up.