You are indeed correct - when it was introduced I understood it was one fare for all the stations but didn't realise it wasn't one fare for travel elsewhere from each station. You learn something new every day.
The point of platforms 13-14 is Southern Reigate services are programmed from those platforms.
Gatwick Express is capable as a Driver Only operation as far as I am aware, although they may have OBS on the trains.
I try not to travel between Victoria and Gatwick on GatEX but I cannot recall any "OBS/Guard" announcements or staff on trains when travelling between Gatwick and Brighton, which I do 2-3 times a month, which of course may be just the journeys I have done.
A couple of times last year I got a GX-branded London-bound train at Brighton in the evening, and in both cases there was an announcement about (alleged) ticket validity,
and a ticket check before Gatwick. My Brighton-Thameslink [ie to a T/Link station destination, not a ticket specifying the use of T/Link services to London] was accepted without question each time, on the basis/assumption that I was changing at Gatwick to a different London-bound train, not continuing-to Victoria, and there were no (alleged) brand restrictions on my ticket, though it was at the same cheaper London-Brighton price as tickets
with that alleged brand restriction. (In fact, my change at Gatwick was to another Victoria-bound train, but one stopping at Clapham Junction so I could change for Waterloo - my intended London Terminal destination - where I exited on the basis I was on a valid route to London Bridge via Waterloo East, for onward travel to a Thameslink Core station; I was of course able to stop short at Waterloo.)