The fans will leave during the night of Saturday to Sunday, when the SBB will be running lots of extra trains. I assume you are travelling on Sunday. Most fans will be home by then.
And trains in Switzerland are nothing like those in the UK.
If you are going to Vaduz you can just book Basel - Vaduz (post) and you wuill discover that the best way is to take a bus from Sargans, not to go to Buchs, as that is actually a detour. I would suggest you take that route, as it is also a single change.
Regarding reservations: In Switzerland 1st class is usually at one of the ends of the train, so you cannot book a middle carriage when you are in 1st class. In the case of the Basel - Chur trains the 1st class is at the Zurich end. The train reverses in Zurich, so you will be at the end of the train in Sargans. You can see that all on www.sbb.ch if you look at the trip details, where you will find train compositions, station maps etc…
Changing from the train to the Bus to Vaduz in Sargans will be a 1 minute walk, with no stairs involved. Changing to the train to Buchs is a slightly longer walk, but also all on the same level.
As to what “side corrideror” and “central gangway” mean: Traditionally intercity train carriages came in two versions: You had carriages with compartments, and a corridor running along the side, and open carriages with a aisle in the middle, and seats on both sides. The reservation systems still allows you to express a preference for one or the other type, but in practice not many trains still have compartments.
My suggestion: Do not bother with reservations. Just board car #3, which will be the 1st class car that is furthest forward in Sargans. Then in Sargans just hop on the bus to Vaduz.