Parking is open at the train station and by the bridge

I believe there is a local "Enterprise Rental" in Charles Town. They "may" pick you up but really not sure. Definitely call them in advance. There is not much in the immediate area of the train station unfortunately and definitely no car rentals. For bus schedules, look up the local transit company, EPTA.

I see it used all the time by plenty of people to travel to dc and wherever else. But i dont know if it runs on saturdays

Two

I would check web site.

I believe it depends on the time, probably not during peak rush.

No long term parking allowed at Harper's Ferry.

No, not really. Just the limited parking in front of the train station.