Will not idle and shuts off after it starts

If it runs smoothly when you hold the accelerator pedal down 1/4", and it runs okay at highway speed, the most common cause of low idle speed is the battery was recently disconnected or run drained. The engine computer loses its memory. Most of that will be relearned as soon as you start driving, except for "minimum throttle". Until that is relearned, idle speed may be so low that the engine will not start unless you hold the accelerator pedal down a little. You will not get the nice idle flare-up to 1500 rpm at start-up, and it will tend to stall at stop signs.

To meet the conditions for minimum throttle to be relearned, drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the pedals.

The poor performance is what needs to be diagnosed. Stalling is to be expected. The first thing to consider is the spark plugs and wires. A MAP sensor can cause poor performance too, but those have been pretty reliable. Next, given the additional symptom of the fuel pump cycling on and off, we might need to look at the crankshaft position sensor and camshaft position sensor. Both of them require a critical air gap to develop reliable signals. We need a scanner to view those sensors and see if they are sending reliable signals. Also consider that low system voltage will affect sensor readings and engine performance. If the battery has one bad cell, besides slow cranking, the low voltage can confuse the engine computer into switching modes between "ignition switch on" and "ignition switch off". Each time it switches to "on", the fuel pump will run for one second. You will hear various relays cycling on and off at the same time.