yes, the hydraulic filters can be very difficult to remove. Search this forum for many discussions. Be prepared with tools, sturdy strap wrenches, and cheaters. And a wrestling match. Check that the mounting nipple is tight into the housing before putting on the new filter. Do not overtighten.
Mght as well use Kubota's best transhydraulic oil. SuperUDT2. Sure, it's overkill for the
L39 tranny, but the money you could save isn't worth the hassles you could have.
I live in a dry climate, the tractor is covered, and I am careful with the fuel I buy. So I never have replaced the fuel filter. I always replace both air filters and the engine oil filter.
I wouldn't be surprised if yours has been sitting that it needs a new battery. They self-discharge, and if they sit long discharged they are never right again.
For the front axle I use any main brand 80w-90 gear oil - which is approx. the same weight as 30 wt engine oil.
For engine oil everyone has preferences. Mine used to be 15w-40 Rotella diesel oil. Now I tend to use a full synthetic in the 15w-40 range. But I've never seen or heard of an engine damaged by good multiweight oil of any kind.
Use a hand lever pump cartridge grease gun on all the zerks. I use JD general purpose polyurea grease "the green grease" just about everywhere.
Good luck,
Go slow take your time & enjoy the project.
rScotty