I would like to disable or remove the warning alarm for the low fuel

You need to start by getting a code reader and checking for trouble codes (DTCs) in order to figure out what's going on. As far as low tire pressure is concerned, batteries in the TPMS (tire pressure monitoring system) sensors inside the rims have a fixed life - you will get warnings like this when the sensors need replacing, and if one has gone dead, you can expect the rest to follow soon.

cancel your alarm and see how the car behaves.

I know that there is a fuse you can pull in the glove box that will disengage the alarm system (i forget which one). Be warned however, pulling that fuse will also disables your speedometer, temp gauge, and fuel gauge, possibly oil level gauge too.

Look for a problem with the fuel level sensor wire or a bad fuel level sensor. It could also be a failure right in the fuel gauge. Your model probably uses a direct metering (analog) gauge*. These have wire-wound resistors inside that sometimes burn out or break. If the low fuel warning light comes on when it's supposed to, then the problem is the gauge itself.

*Some of the newer GM models starting in 2001 have replaced analog gauges with digital circuits using stepper motors to drive the gauge needles, and they've had reliability issues with the stepper motors.

2005 Instrument cluster layout

1. Speedometer
2. Brake warning light
3. Turn signal indicator light
4. High beam indicator light
5. Malfunction Indicator Light (MIL)
6. Airbag warning light
7. Anti-Lock brake warning light
8. Tachometer
9. Security alarm indicator light
10. Oil pressure warning light
11. Electronic Stability Program (ESP)/
Traction Control System (TCS) indicator light
12. Tire Pressure Monitor warning light (base)

13. Temperature gauge
14. Electronic Vehicle Information Display
15. Tow/Haul indicator light
16. 4WD Low mode indicator light
17. Seat belt reminder light
18. Cruise control indicator light
19. Odometer/Trip Odometer
20. Transmission gear indicator
21. Fuel gauge
22. Electronic Throttle warning light (5.7 Hemi)
23. Front fog light indicator light
24. Voltage warning light

It sounds like your starter Kill switch is engaging. If you have an after market alarm installed cut the power to that by removing the in line fuse or cutting the power wire. If the alarm was part of the vehicle, which sounds possible based on your post, you can try resetting the ECM by removing the Negative battery terminal for 1 min then reconnecting. There should also be a fuse for the alarm in your fuse panel. If you remove that it should disable the kill switch.

The current to the sender can't be allowed to be DC because it could spark and blow up.
So they use a ******** or oscillator to turn it into AC. That could be the problem. It is usually mounted near the gauge.

Check the ground wire, could be corroded.

You have a fuel gauge sending unit problem, the gauge is not the problem, the sending unit is in the gas tank, u must remove the gas tank to replace it.

Depending on the severity of the problem, Sea Foam fuel additive can fix this (or at least lessen the crazy jumping around). It's available at NAPA. It worked on my Jimmy. However, in my case gauge started jumping around with less than 1/4 tank (worked fine when full).