What should the fuel pressure be for a 2002 Chevy Malibu?

That should be about right at idle.

I just have one suggestion, after what all your mechanic already did. I would want to know the fuel pressure reading WHEN IT WON'T START. So you would need a fuel pressure gauge handy, for that time it won't start. Hook up the gauge and turn the key on- if at 59 psi, when the engine won't start, then you know the fuel pump and the relay sensor is not the problem. And so probably not a fuel problem, although you haven't checked the injector circuit, but likely that wouldn't exhibit a problem as you have.
So if not a fuel problem, check for spark when it won't start. Maybe the problem is in the ignition system. Buy a spark tester from a parts store, use it when the **** engine won't start- simple and easy check of your ignition system.

To check your fuel pump,Connect a fuel pressure gauge to the fuel pressure test port connection. Turn key to on and reading should be 30 to 45 PSI.The valve to connect gauge is on fuel rail at fuel injectors.It has a cap on it,you have to remove.

There is a fuse for ther injectors. There should be a constant power to the injectors. the computer is what grounds them out. So it's not the computer. Also check the asd relay. Auto shut down.

check to see if you have fuel pressure-check fire at spark plugs.

Just had a new fuel pump installed in 2002 Chevy Malibu. Worked great for about a week and then the fuel gauge started reading "empty" when the car has a full tank of gas. What happened?

Sounds like a leaking fuel pressure regulator. After it has been replaced change the oil and check for oil leaks.

ther pressure and return lines are probably reversed at the sending unit

Cheak your fuse under the drivers side under the hood. Look in your manuel for fuel fuse. It looks like a little black box.

Check the fuel pressure when it won't start also check for spark when it is not starting