Regional trains are like commuter trains or city buses. No reservations needed, no seats assigned, they are on a first come first served basis (you may have to stand up if full).
As noted above, Regional train tickets have a validity of 4 hours from the moment you stamp them at the machine before boarding. You must complete the trip within that time.
Also since August last year, when you buy a Regional ticket you must specify the date you will be using that ticket. If you don't use it on that day, the ticket becomes invalid.
Hopping off and on is possible only if the entire trip is completed within 4 hours. Therefore that allows for short stops only along the way.
Freccia trains (high speed) work exactly like airplanes. The ticket is valid for a specific train and you have a specific seat assigned. You can't hop on and off them. You need a separate ticket with seat reservation for each specific high speed train you board.
A rail pass rarely makes sense in Italy, price wise.
But my question is: what's the big deal about buying a separate ticket each time? At the automatic vending machines it takes only seconds.