Well, I'll chime in with what I know:
The tire pressure monitoring system (TPMS) alert you are seeing on the DIC will not clear until you put functional tire pressure sensors back into the wheels and
reprogram them into the TPMS. Take care to purchase the correct tire pressure sensors for your vehicle; the early C5's (1997-2000) used GM P/N 25981210; I believe that the later tire pressure sensors (GM P/N 25773946) are incompatible.
For that matter,
none of the alerts will clear until the cause has been corrected (presuming the DIC itself isn't on the blink). I'm suspicious that the other alerts you're seeing are related to the modifications made to the vehicle; they may also be a result of sensors that have been removed or are not 'playing well' with the after-market equipment. But that's just speculation on my part...
The flaky oil pressure gauge readings are probably the early symptoms of the gauge sensor dying on you. This is a relatively common issue with the C5. Search the forum for one of the numerous threads dealing with that topic and the trials and tribulations on replacing one (should you care to do so yourself). Even if you don't want to do it yourself, it's good knowledge, as there are some tricks to replacing it properly (i.e.,
without drilling holes into other parts of the vehicle just to gain access to it...).
Key fob may be as simple as a dead battery; that was my problem when I bought my '98 coupe last year. See page 2-13 of your Owner's Manual on how to replace the fob battery. After replacing the battery, you may need to resynchronize or re-match your fob to the car; see page 2-11 of your Owner's Manual for information on that. In fact, you might even try resynchronizing/re-matching the fob(s)
before buying a replacement battery.
These earlier fobs also had a 'passive' feature, where the vehicle sensed the presence of a nearby fob and unlocked the vehicle without the need to press the buttons; similarly, it locks the vehicle after you leave the vicinity of the vehicle with the fob. As an aside, I'm guessing this feature requires battery power to scan (either the fob for the vehicle, or the vehicle for the fob), and whenever they're both within communication range of one another, they keep communicating, draining the battery prematurely. There's a little slider (see p. 2-8 of the Owner's Manual) on the fob that allows you to deactivate the passive feature, and there's a vehicle setting (accessed through the "OPTIONS" button of the DIC -- see p. 2-94 of the Owner's Manual) that works in concert with this feature. Oh, and like the tire pressure sensors, I believe that the later C5 key fobs (no 'passive' feature slider on the fob) are incompatible with the older C5 vehicles that had this feature. So if you have one of the newer C5 fobs, that's probably the reason it won't work...
