Welcome to TBN...
You are asking good questions... and listening for the right answers.
OK...my best advice is for you to get somebody to walk with you thru the tractor, its fluids, where they go in, how to check their levels, where the grease zerks are, etc. I applaud your interest, initiative in posting on TBN, and gumption to get out there and make things happen :thumbsup:
I suspect that there are reasons that maybe your father has not been able to tell/show you the above. I understand, my dad is 97 and no longer able to do the things he once did.
A brief tutorial re fluids
Oil goes into the engine ..this us 10 W 30, similar designations. Gasoline engines take one kind of oil. Diesel engines take a DIFFERENT kind of oil. Be sure and ONLY use the kind of oil for the engine you have....These kinds of oil are formulated for the high heat of a combustion engine.
Hydraulic fluid is used in the hydraulic cylinders to push them in and out, pass thru hydraulic pumps, hydrostatic transmissions, other types of gears.
There are many differences between the various kinds of oil. You should pay specific attention to the "weight" of the oil recommended for the various parts of your tractor and equipment such as the bush hog.
Yes, the bush hog gear box will take gear oil...NOT engine oil and NOT hydraulic oil.
About the tractor bogging down when the bush hog has to work hard. Likely this is not an oil problem, but rather an operator gearing/throttle problem. Keep your RPM's high when bush hogging...even when in heavy grass/brush. Achieve this via the throttle and gearing down so the tractor moves more slowly thru the stuff you are cutting.
Again, this is not the kind of thing that is best explained in a post, but by someone who can hear what is happening, understand the questions you have, and show you the specifics of where too oil, how to test fluid levels, how fast to run the tractor when it is working. These things are not hard to learn, but it is a little different from driving a car where you just get in and go. It won't take you long to learn this, we each have had to learn it for our own specific tractors.
Hope you can find that someone.