I suggest using the SBB Mobile app, it is the easiest way to buy tickets. There, you can enter a connection, then, the class upgrade is offered among other “Additional offers” (tickets), see screenshot below.
No, on normal routes (except most mountain railways), the STP is your ticket. There is no need to buy additional tickets, you can simply get on/off trains, buses, trams, etc at your leisure. Swiss public transport (again, except for some PE trains) uses a free seating system, seat reservations are not required. For mountain railways, your STP often grants a reduction of 50%.
In my first reply, I forgot to add the link for the Swiss Travel Pass validity map: https://www.mystsnet.com/areaofvaliditymap2023