Do I need new hoses or can I reuse the originals?

Reuse your existing hoses if they're in good condition — overflow routing matches OEM spec. If hoses are cracked, hardened, or weeping, swap them while the tank is out; you'll save yourself a repeat job later.

Will I need to drain the entire cooling system to install this?

You don't need a full system drain. Disconnect the overflow tube and radiator inlet line at the tank only, swap the unit, and reconnect. Top off coolant after install and bleed air as needed per your service manual.

Is the cap included, or will I need to transfer mine from the old tank?

Pressure-rated cap comes with this assembly — you're not transferring anything. Install as-is and you're done.