Depending upon what size the carb air inlet is, for offroad/trail riding you'll want to use one of THESE and one of THESE. Oiling the foam filter with foam filter oil is recommended.
I'm surprised there isn't an oil drain plug in the bottom front or back of the engine, like on a snowthrower or rototiller. I thought that was the setup you were working with, not the conventional bottom drain bolt like on a car or truck.
Below is a modified version of the 00'-03' XR50/70 wiring schematic, giving you a basic idea of what wires go where. The Chinese engine wire colors should be similar.
Check your engine case breather hose and make sure it isn't kinked or clogged, pressurizing the cases and possibly pushing the engine oil into the cylinder and/or head and out the exhaust valve.
looks like pieces of the steering neck are broken off and missing. Clicking on the pics to open and/or enlarge them didn't work for me, to get a better look.
I would degrease and clean the entire engine, let it dry after a mild rinse, and then start it to see exactly where it is leaking oil, and go from there.