cocktail,
The new schedules are usually uploaded about 15 June. As the previous reply indicated, most of the trains you'll be using will probably be Regionale and the schedules won't be much different than what they are now. I'd suggest checking the current schedules within the next week, using the same day-of-the-week that you'll be taking each of the trips. That will provide you with the details and a close (if not exact) time for each departure.
As most of these are Regionale, there's no reason to pre-purchase as there won't be any difference in price. It's sometimes difficult to pre-purchase Regionale tickets online so the easiest solution is simply to buy them when you arrive in Italy, either at a staffed ticket office or from a Kiosk (they have English language option).
For boarding and disembarking trains, there are usually only a couple of steps. If you can lift the luggage onto the train and then haul yourself on board, that should work (it would be prudent to pack light). However you'll have to be quick as there's usually a bit of a "crush", with people trying to get off and on the trains at the same time. If you'll be taking larger luggage, there will be a rack at one end of the car for storing the bags. If you have more compact luggage, I'd suggest keeping it at your seat if possible (there are racks over each seat, so you'd have to lift it up there). Be sure to keep an eye on luggage stored in the rack.
"these are long train rides unfortunately but have no choice"
Actually, the trips you mentioned are not long at all. For example.....
- Firenze SMN to Perugia - ~2H:15M via Regionale Veloce
- Perugia to Assisi - ~20 minutes via Regionale Veloce
- Assisi to Orvieto - ~2H:15M via Regionale Veloce / InterCity
- Orvieto to Roma Termini - ~1H:15M via Regionale Veloce / Intercity
One other point to mention with Regionale trains, is that you MUST validate your tickets prior to boarding the train on the day of travel. Failure to do so may result in hefty fines, which will be collected on the spot!
Regarding the Taxi issue....
- Perugia - there should be Taxi's waiting outside the station.
- Assisi - again there should be Taxi's at the station, but in this case I'd suggest making arrangements with your hotel and they'll have one waiting for you (that's what I did last year).
- Orvieto - you could use a Taxi from the station or take the Funicular up the hill, depending on the condition with your legs.
- Rome - if you walk straight ahead (with your back to the tracks) and out the front door, you'll find LOTS of Taxi's waiting in the rank. Take the next one in line.