Will this radiator work if my vehicle had the towing package originally?

No. This is spec'd for non-towing models. If your Camry came with factory tow capability, verify your original radiator type before ordering — they're different units.

Do I need new hoses or clamps when I install this?

Hoses and clamps are not included. Inspect your existing hoses during installation — if they're cracked or brittle, replace them at the same time to avoid future leaks.

Can I reuse my existing coolant, or do I need to flush the system?

Flush the system before install. Old coolant may contain debris from your failed radiator. Fresh coolant ensures proper heat transfer and protects your new unit.