What oil and how much for it? - Kymco 2005 Mongoose 250

Check the oil for proper fill.. I believe you have a low oil level switch that kills the spark to protect the engine,. If you have the oil to full on the dip stick look for the low oil pressure switch and short out the 2 wires to each other or if it's a single wire disconnect it and see if you get spark.. if you do replace the oil pressure switch or add the oil to proper height should help..

You can use 10-40w motor oil. You don't have to waste your money on special gear oil made just for motorcycles. There isn't anything special about those so called gear-oil type oils.

Is it full at present? If so, drain the oil and measure the volume.
If you are changing the oil it might a good idea to change the filter as well. Before you begin, run the engine for a few minutes to heat up and thin the oil so that it runs out easily.

you dont, you replace it!
most likely not failed, you need to turn over the oil pump 50 to 150 revolutions per drop of oil! check it again!

you can pull the oil tube off the carb for a couple seconds while its running to see if it drips oil. I'd run a synthetic 2 stroke oil, lubes better and burns cleaner.

That's sounds strange?
Oil can only leak out or the engine is burning it.?
If its burning your oil valve stem seals are worn it lets oil into your combustion chamber and burn it.
Maybe get a local mechanic to take a look.
Good luck

pump is suffering excessive oil pressure
you are very short on the details of the failure --broken shaft , gears , chain housing etc but I would be checking oil passage blockages, faulty pump pressure regulator spun bearing that the pump feeds into the oil galleys

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Use heavy duty SAE 80W-90 gear oil

Engine oil does work but the oil will not last as long nor will it protect the bearing's/gear's as well as gear oil. Thick dif oil can work to.
Also the gear box is should be sealed.