For info on changing the hydraulic fluid, check out tips 3 & 4 at the link below.
Resist the temptation to save 5 minutes by parking it nose down in a ditch instead of draining the fluid. The front transmission seal was not designed to be totally immersed in oil. If it's defective, you will fill the bell housing with oil and then you will get to replace the clutch.
With all of the fluid drained out, block the front wheels & get the rear wheels up at least a foot. (you'll see why soon enough) Remove the 4 bolts holding the PTO shaft in & pull it to the rear & out of the tractor. Loosen all of the bolts. Remove all but 2 corner bolts. Then, carefully remove them. If you are lucky, the pump will drop free (and dump a pint or so of hydraulic fluid down your sleeves). If not, wrestle it free. The pump has 'ears' that fit into the housing; wiggle it a bit & it will drop free. If you have the rear tires a foot or more off of the ground, you will have enough arm room to hold the pump & lower it at the same time. Put it on your work bench & remove the safety valve (p/n 638) and the control arm lever (p/n 643) which will allow you to remove the intake & exhaust valves (p/n's 640 & 698) Drop all of it in a bucket of diesel (or mineral spirits) or your parts washer & let it soak overnight. Once it has a good soaking, get it on the bench & start blowing it out w/ compressed air. Run cleaning fluid into the hydraulic discharge near the test port & make sure you get a good flow out the small hole in the side of the pump were the control valve fits. I don't see much need to pull it down any further just to clean it. But, I always replace the safety valve (p/n 638, about $25) Reinstalling the pump is harder than pulling it out because you have a gasket to worry about. (no sealer on the gasket) And, you will probably need a helper to guide the control rod into the pump rocker shaft unless you've done this 6 or 7 times before!
Put some grease on the new pto seal.
Contrary to conventional wisdom, not a lot of water gets in the oil from the shifter boot. Of course, if it's bad, replace it, but you get water from the draft control spring & the dipstick. But, most water is just a byproduct of the heating/cooling cycle of the oil. I've seen the pictures of an experiment to test the 'leaky shifter boot' theory. With no shifter boot installed, a lot of water was poured over the transmission cover sitting over a 5 gallon bucket. Result? No water in the bucket.
You'll need a pump gasket, safety valve, inspection plate gasket(s), PTO seal, PTO gasket, gasket sealer & 5 gallons of fluid to do all of the above.