No need for a filter just put new clean fluid in it and call it a day. Bleed it with the front end up in the air and turn it lock to lock around 15 times to get the air out. Keep topping off the pump during this. Once it stays full and has no bubbles in the fluid take it for a drive. Check the fluid level again once it cools down and top off as necessary.
Yep, car running. It will likely whine for a bit until most of the air is out. I try to turn it as fast as I can just to make it work hard.
Good luck. I wish it would warm up here. I don't even want to go out in the garage and work on the 02 Cadillac sitting there. I can't work well in a 25* garage.