Some people attach a vacuum cleaner hose to the fill hole. The suction keeps most of the fluid inside the tractor for easier filter changes. If no vacuum you have to be quick changing the filter. You will lose a couple quarts that you'll need to top of with when done.
I doubt it. I've pulled and cleaned a few JD suction screens and they are all down low. If this is your first filter change The screen should be good. Wait till you need to change fluid to pull and clean.
Cancel that, just saw yours is a 2001. If you need to clean the screen you may as well change the fluid.
If you have over 670 hours since the dealer last changed the fluid due to the repair I would change the fluid, filter, and clean the screen. But that's what I would do. I personally don't go over 400 hours between changes. If there's a way to pull and clean the screen without changing the fluid I don't know how to do it.