Well what you have posted proves you have absolutely no idea.
So lets start with something simple.
Take a DC reading between the battery posts engine stopped.
Start the engine, let it run for a minute or so at FULL Speed and take another reading
Post what you found.
While you are there multimeter in hand take an AC reading as well.
AC should be 0 DC should be >12V engine off & >13 V engine running.
If your mower has an electric PTO take a third battery reading engine running full speed and PTO running.
It should also be better than 13 V DC.