The only concern you might have is oil-fouling on the sparkplug.When an engine is turned upside down the oil from the crankcase seeps around the piston rings into the cylinder head and out any open valves.Into the carburetor via intake valve,or exhaust manifold via exhaust valve.It will eventually dissipate.
Stuck floats or dirty needle valve.
No, you can charge it on the mower and you do not have to remove it or disconnect the cables.
It is a small electrical thing on the bottom of the carburetor. It will have one or two wires going to it. It shuts the fuel from getting through the carburetor when the key is off.
If you have to turn the choke on a little, the motor is starving for fuel. need to clean the carburetor
Disconnect the solenoid wire, turn the bowl counter clockwise. No tools are needed.
Can I do it myself, set the timing on my riding mower.
it may not have one. If it does it will be located on the fuel line between the fuel tank and the carburetor.
Fix it.
Any good lawn mower repair shop should be able to order just about any brand of mower part for you. Good luck.
It is not totally unusual. It should not happen though. It means that your carburetor is leaking gas through while the mower is not running. It will fill the cylinder and get into the oil. A quick fix is to get an inline gas shutoff valve and just shut off the gas when you are not using the mower. Otherwise you will need to rebuild the carburetor to fix the problem. You will also have to clear out all the gas from the cylinder and if it got into the oil you will need to drain and change the oil.
you tube how to clean a mower carburator.
john deere smallest riding lawn mower