At first blush you have a completely worn out and wasted Airhead.
We will have to see the cylinder head, disassembled, and the connecting rod bearings and the crank shaft, well lit photo please of condition of crank journal.
The crank shaft is replaceable but they can be hard to find. Labor for putting a new crank shaft in will be about $500 (sorry that ones a guess really. A friend had this done two years ago but he never told me what it cost). The problem is the main bearings and thrust bearings. Tools for doing this are not the DIY type of tools.
Same for the heads. Tools to fix them will cost more than what it costs to have it done. It will cost close to $500 to fix the heads.
You are going to need the special socket to take the connecting rods out. This should cost you about $10.
The valves come apart with a valve spring compressor. This will cost anywhere between $25 and $45.
Engine oil is not "black" from burning up. It is black from mileage. There is one thing that never changes. You want to learn to be a mechanic then learn to change the engine oil. The oil is the life blood of the engine. The oil is cooling and lubricating the engine. Two things that are absolutely necessary for the engine to live. There is another side to life. It is death. When the oil gets old an engine wears rapidly. Too much wear and the engine dies. You were thinking maybe it was just a little tired?
You may have been able to save this motor if you had changed the engine oil when you first got it but it sounds like the former owner didn't treat it any better than you did. The oil was already old. If not now this motor would have blown soon.
Send pictures of the debris in the oil filter. Take the oil pan off. Send pictures of debris in oil pan.
How's the transmission in this bike? Maybe you are in the market for another engine. Usually a much cheaper alternative to fixing something like you have described.
edit; It's a good idea to fill in some info on your profile.