Do I need new hardware to install this, or does it use the original bolts?

You'll reuse your existing mounting bolts and fasteners. Just have them ready and check that they're clean and not damaged before reassembly.

Should I replace the wheel bearing on both sides at the same time?

If one side is worn enough to need replacement, the other is likely not far behind. Doing both at once saves labor time and prevents a second job soon after.

Can I reuse the old rotor and brake pads with this new hub?

Your existing rotor bolts to the new hub the same way it did to the old one. Pads stay in your caliper. Inspect both for wear while you're in there, but you don't have to replace them unless needed.