Do I need to replace both sides or just one?

Hubs wear independently. If one is bad, you can replace just that side. If the other is approaching high mileage, many shops replace both at once to avoid a second job soon after.

What mounting hardware comes with this?

This is the hub assembly itself. You'll need the bolts that hold it to your knuckle—those stay with your vehicle. Check your service manual for the correct fastener spec and torque value.

Can I reuse the brake rotor and wheel bearings from my old hub?

The bearings are sealed inside this assembly, so they're not serviceable separately. The rotor bolts to the hat of the new hub—if your old rotor is in good shape, it'll work. Inspect it first for scoring or runout.