i would say the gauges failing are probably unrelated to one another...but just in case, always start with the easy stuff first...such as checking for blown fuses.
next, i'd check sending units for both the fuel and temp gauges.
does your speedo still work? is your ABS light on? for the odo/tripo problem i would say its probably a failed VSS, but if thats the case it should take out your speedo as well and possibly trip the ABS light.
the door dinger failing to shut off is due to a sticky door switch. the switch is attached to the inside of the door latch, inside the door. you can try hosing it down with some lube (try to spray it down inside the latch)...but if that doesnt free it up you'll have to pull the door panel off and free it up by hand.