Welcome Fossil Rock!
Yes, it should charge it's own battery unless there is a problem in the charging circuit. It might be since you are having such a hard time to get it started it is just running the battery down lower then what it has time to charge it back up. The charging circuit does not put out a lot of amperage and it takes some time (maybe a couple of hours or more to throw out a number) running at full throttle to recover after being drained down beyond the point of it being able to turn the starter.
As for the hard start issue, have you checked the flywheel key closely to make sure it is not dented/partly sheared?
Yes, it should charge it's own battery unless there is a problem in the charging circuit. It might be since you are having such a hard time to get it started it is just running the battery down lower then what it has time to charge it back up. The charging circuit does not put out a lot of amperage and it takes some time (maybe a couple of hours or more to throw out a number) running at full throttle to recover after being drained down beyond the point of it being able to turn the starter.
As for the hard start issue, have you checked the flywheel key closely to make sure it is not dented/partly sheared?