I see this has gone for a couple of days without anyone making suggestions, so I'll do the best I can here.
1. Drain plugs. You don't say why they won't come off. Are they frozen or has the head been rounded off or what? If they are just frozen, you might try some penetrating oil and some gentle tapping with a drift.
2. The strainer is hard to find and the picture in the shop manual is not very helpful. It's on the right side of the tractor, inboard and a little behind the big spin-off trans filter on that side. There is a bunch of plumbing up in there with similar hex-head bolts and end caps, so you may have to figure out which one it is by trial and error. My tractor is a different model than your 3010, so I can't describe what yours looks like exactly. I don't think the TNT would change the layout any, however.
3. Oh yes, the filter. It's a bear, allright. They all seem to come from the factory like that. Kubota must have the son of Godzilla installing the filters on the assembly line or something. If you search this forum, you may find some interesting innovations people have tried to break them loose the first time. My approach involved a strap wrench, a tow cable and the hitch on my truck. This was probably not the safest thing to do, but a short tug - just a few inches! - did the trick.
4. Don't know about the magnet. I guess they have it to catch any particles of metal. That's probably a good thing.
It sounds like maybe the juice in your 3010 has never been changed. How many hours do you have on it? Although the factory recommends regular changing, some dealers will say that if the fluid is not low and doesn't look discolored from overheating, it should be OK. I would rather play it safe myself.
By the way, welcome to TBN! I hope there is something here you can use.