There is a drain plug. It is NOT the one on the left side bottom of the engine towards the front, it is the other plug on the bottom. I don't know what the bottom plug on left is but don't open that one, parts start to come out with it! You are correct, the engine oil and transmission/clutch oil is all the same, fill cap on the right side top.
I bought a new carb off ebay for like $10 and a key assy and switch from this site. Thing started right up with new battery.
Buy Kazuma Replacement Parts at Kazuma of America - Falcon 90 (Mini) (kazumausaparts.com)