2003 jeep grand cherokee power cuts out when driving along with wrong key light coming on and fuel guage goes to empty--in a few seconds it comes back to life

Could be the auto shutdown relay is getting weak. Try swapping it with the horn relay.

yes it may be ur computer problem

try to off it for few hours and then ON it

if the other light is ok and the fuel gauge is only dead, may be you have no more fuel, try to refill fuel, if the battery is also dead replace new battery.

The most common cause of this problem is that the gas gage sending unit that senses the fuel level is defective, it is an open circuit. The sending unit is part of the fuel pump module and all comes as one part. To replace the fuel pump module you must drop the fuel tank out of the truck.

If the check engine light comes on then there must be a trouble code stored in the PCM memory. What is the code when you turn the key on,off,on ,off... then leave it on....count the engine light blinks. (Don't start the engine during the key procedure) each series of blinks will be a digit.

go to advance auto part or autozone to have them check your alternator.

possible fuel pump

fuel pump may be out but you have to drop the tank to fix it

This will be challenging to find ... If headlights dim or flicker too ... check battery terminals first. But I think it will be a large harness with quite a few wires on it ... Check ... for loose bulkhead connectors at the firewall ... and between the Engine and the body/firewall .... at the ECU .... you may also check for loose harness connectors at the fuse box. check for loose or corroded fuses ... especially if a cover is missing.
If I remember correctly this truck has 3 fuse panels in it. Check the manual

the sending unit is more then likely a mess, take it back to where you bought it and demand they fix the problem