Will this pump work with my stock washer reservoir?

Yes. This pump is designed for factory mounting points on the OEM reservoir — no adapters or modifications needed. Line it up with the existing outlet ports and you're good.

Do I need to drain the reservoir before swapping this in?

You don't have to, but it's easier if you do. A dry or nearly empty reservoir gives you more room to maneuver the pump out and the new one in. Either way, test spray both circuits before you call it done.

Does this pump come with new hoses or connectors?

Just the pump assembly. Reuse your existing washer lines and reservoir connections — they'll fit directly. Inspect the hoses for cracks or hardening; replace them if they look sketchy.