Have you got an EML Check Engine light? It would be good to check any fault codes on the ECU with Protune 2 . A P0170 or P0173 "Adaptive maxed out" code will indicate that the fuel pump is on the way out, as will a pressure check of the fuel system. As the car has not been used for some time, the Throttle Position Sensor can get oxidation on its wiper and cause running problems with random signals, usually a P0122/3 code. The fault codes will indicate any other engine sensor issues as well.
The random fuel level indications are normal, particularly if the car is not used. The resistance wires inside the level sender unit in the RH tank need to be cleaned with very fine abrasive and then a more stable indication should be shown, for a year or two maybe.
I would say that a fault codes check, a fuel pressure check and a check of the battery condition would be good things to do before getting too deep. If you don't have a Walbro fuel pump fitted, you should have. The pump is the most likely cause of your problems. Detailed pump replacement instructions are in the owner resources at the top of this forum.
