tk,
Lots of good suggestions so far, and I have a few thoughts to add......
This video is a bit dated, but it will give you an idea of what to expect - https://www.youtube.com/watch?v=Q7whfEiZp34 . There's also this website - https://www.theitalianontour.com/how-to-travel-by-train-in-italy-a-locals-guide/ .
As you may be aware, tickets for the express trains such as the high speed Freccia come with compulsory seat reservations. Those will specify your Carozza (coach no.) and Posti (Seat no's.). Also, you must take the train specified on the ticket. If you board any other train, even by mistake, you'll be subject to hefty fines which are usually collected on the spot.
There is no reserved seating on Regionale trains. As you've bought online tickets for the Regionale trains, you won't have to validate these. However if you buy any tickets locally at the kiosks or whatever for Regionale trains, for Metro or Buses, you must validate these prior to boarding on the day of travel or again hefty fines. That also applies to Vaporetto tickets in Venice.
There are luggage racks at one end of the coaches. If those are full, you can often put bags in the "A" formed by the backs of two seats. Smaller carry on items are best kept close, on the racks above your seat.
Regarding your questions.....
- Yes, generally speaking. As I recall, you'll have to pass through a security barrier at the stations to reach trackside. The platforms are referred to as Binario. There are always large electronic displays with all the arrivals and departures listed, and also large paper charts. You might find this look at Firenze SMN to be helpful - https://www.youtube.com/watch?v=7AvG8bgyxYo .
- The people you'll likely be interacting with such as ticket agents, onboard staff, etc. usually speak reasonably good English. You may find this helpful - https://www.ricksteves.com/travel-tips/sightseeing/language-barrier .
- As you're not too familiar with things yet, I agree with a previous reply that arriving 20 minutes early would be prudent. Having extra time will also allow you to buy a Panino or beverage at one of the many shops in the station.
As you'll be changing trains at some stations, that often involves going down to a transfer tunnel, in order to get from one platform to another.
When you arrive at Siena, the station is at the bottom of the hill so you'll have to take a taxi or bus up to the main part of the city.
When you arrive at Roma Termini, you may have to take a taxi to your hotel (depending on which hotel you're using). There are always taxis waiting right outside the front doors of the station. I often have a note with the name and address of my hotel, so there's no confusion. There's good information on transportation in Italy in the Rick Steves Italy guidebook.
Buon viaggio!