Starter is not a likely cause. If it starts the car, it has nothing to do with the engine once it is running. Fuel pump is doubtful, unless the fuel filter is clogged and it has been overworking itself for any period of time.
The air filter is not located in the fuel injection, it is located in the airbox, which feeds the intake manifold. By fuel injection filter, I take it you mean "fuel filter"? Yes it is possible that the fuel filter could be partially clogged and needs replacement. If you don't remember when it was last replaced, pick one up. However, if it has been replaced in the last year or so, it should be ok. Lastly, yes, bad gas could cause problems like this if the car has been sitting and not running for long periods of time. When was the last time you filled up the tank?
Yes, should be CFI, or TFI as others call it. Basically a fuel injector pointing down into a throttle body.
87 octane is fine for an older car like this. 89 wouldn't hurt if you think the fuel system might be dirty. I would also pick up a couple of cans of fuel injector cleaner.
Besides the other things I mentioned, you should check (and replace if needed) the condition of the following: spark plugs, spark plug wires, distributor and rotor. Just basic tune-up items. If this engine is a 1.9L, I would very strongly recommend you to take the timing belt cover off and check the timing belt, even if it has nothing to do with your problem. The timing belts are known to break on these cars religiously around every
The idle issues could be a number of items. Make sure all vacuum lines/equipment are tight and functioning properly. All EGR equipment/lines are tight and functioning. Test and clean the idle air control valve, might be stuck if dirty or malfunctioning. All of these things can affect your idle. Inspecting/repairing these systems you might get lucky and discover why it is stalling.
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