Well, first could you create a sentence that does not run on please. I am having a hard time understanding what you are writing. Please use punctuation. Thank you.
Ok. When you turn your ignition on the sound you hear is the fuel pump priming.
You start the car and from what you wrote your car will run, then sometimes shut off.
Right?
The fuel pump should be heard while the engine is running. That is correct. I don't think its your relay. Because your fuel pump would not pressurize the system if the relay was bad. You are jumping to an electrical conclusion and probably haven't ruled a couple of things out. You are getting a connection to the pump, so how can it be an electrical issue. Personally I would change the relay last as an added insurance bonus.
Try looking at the fuel pump connections underneath the rear seat on the passenger side. (Right Hand Side, if you are from another country). Make sure it is snug otherwise connected. Also replace your fuel filter, if you have not done so recently.
We know you are getting fuel because your car runs for a little bit then shuts off. I could be bad hoses underneath the intake manifold. Check your hoses. Make sure they are not cracked and dry rotted. Make sure the ones connected to the ICV (Idle Control Valve) are in good condition. Just because the car runs then shuts off shortly there of doesn't mean its electrical . Make sure that your MAF(Mass Air Flowmeter) is connected.
Even make sure that your oil cap is seated and that the oil dipstick is seated. This engine runs more effeciently with a good vacuum. Make sure the intake bellows is secure as well. In the Army we call this PMCS. It stands for Preventive Maintanence Checks and Services. Do a good PMCS and you will see the payback from this outstanding car. Good Luck.
I truly hope this helps resolve your issue with your car.