Are you certain about the model year of your car? The final MY for GT was 1991. From 1992 all 928s were GTS, so if you do have a 92 it's one of the very rare RHD manual GTS. As you say, the GTS body was different with the flared rear arches
The GTS came as standard with 17" wheels, with the offsets you've described. The wrong offsets you had on the original 17" wheels that came with your car would have had a bad effect on handling, tram lining etc.
The tyre pressure monitoring system was introduced in MY89 on the 928 only, having been tried out on the 959! It was discontinued by start of MY93. The first couple of years of GTS were equipped with RDK, and with 17" wheels that would have been set up for 36psi all round. The 16" wheels ran 36psi front, 44psi rear so you can at least use sensors — they're switches strictly — on 17" fronts from 16" front wheels.
People have successfully run 18" wheels on 928s, but it's not recommended! This article from Angus Fox's 928.org.uk page has chapter and verse on 928 wheel sizes, designs, offsets etc:
https://www.928.org.uk/articles/60-wheels.htmlJust curious about where you found set of Cup 1s which are specific for 928s with those offsets?
On the fuel pump relay question yes they are the relay most prone to failure, as they switch the highest current. The other suspect relays are for ignition (EZK) and injection. You may have intermittent fuel pump relay so see how the new one behaves, after which we can look at other possible causes for cutting out. With 928s an awful lot of mysterious problems are solved by replacing one or more of those three critical relays.