I'm sure someone on here has a service manual, and can give specific but the information I have is that the K3B engine takes 3.5 liters at an oil change, so you'll need 4 quarts of oil. In practice, I've learned all my little tractors take more or less a gallon of engine oil.
I run Shell Rotella 5W40 synthetic diesel oil in everything I own. It's specified for my motorcycles, ATVs, pickup, and the tractors. It's easily available at Wal-Mart and quite affordable; conveniently, it comes in gallon jugs. It makes the math easy: at oil change, each tractor takes a jug, my sportbike takes a jug, and I use any leftovers in my ATV or KTM dirt bike.
Any diesel rated 15W40 oil will be fine in your Beaver, but even in warm California (where blossoms are beginning to break on some fruit trees this week!) the lighter 5 weight synthetic oil is noticeably easier to start cold.
The oil filter will be a Napa 1334 or equivalent; those fit many of the other compact tractors too.
I run whatever 85W90, 75W85, 75W90 etc gear oil is on sale in the front axles. It doesn't really matter that much. They're all about the same viscosity at higher temperatures as motor oils or the hydraulic fluid in the transmission:
Many run the same hydraulic fluid as in the transmission housing to cut back by one type of fluid. I don't think that's wrong, but it doesn't bother me to have an additional type of oil to change, and I also have a (wrongheaded) ulterior motive: The gear oil is thicker when not at operating temperatures, so the axle seals don't really leak much, they just sort of leach a bit. I'm afraid that if I ran something else, they would leak more, and I would have to fix it. :laughing:
I think the capacity will be somewhere between 2.5 to 4 quarts. I'm not sure, since I haven't replaced the non-engine fluids in my ST1440. But my next size up Yanmar 186D calls for 3.5 quarts, and I have a manual for a Ford 1210 of the same size as the Beaver, and it calls for 1.5 liters in the axle housing, and another .2 liters in each gear reduction case, or about 2 quarts overall.
For hydraulic/transmission fluid, run something that is equivalent to John Deere 303, International Harvester (IH) Hy-Tran or several others. Most will list those. It will say something like "Universal tractor fluid." Make sure to pull the filter screen in the suction line and to clean it well.