My 2003 Jetta 1.8T has turned off a couple of times while at a red light.

So my fuel gauge doesn't work, hasn't really
worked ever since my mechanic replaced my fuel
pump. It will show that I have a full tank then later it
will be below half the tank. So I never really know
how much gas I have. I'm always pumping gas to
make sure it's never empty. The other day while I
was driving, I got off the freeway and was at a red
light when suddenly the car just turned off. At first it
didn't want to turn on then it did. I drove it some
more and then the my fuel light came on. It turned
off once again, this time it didn't want to turn on. On
the 3rd try it finally turned on and I took it to a gas
station. I pumped gas and the car turned on like
normal. Ever since then the car was fine. I lent my
sister the car the other day and when she was on
the freeway, the car turned off on her once again.
She pulled to the side and on the first try was able
to turn it on. Drove it home, didn't turn off. She had
pumped gas beforehand. Filled up the tank. Today I
took the car to my mechanic and he said that the
car is fine. That the only thing that popped up in his
computer was that we had used the car without
gas. I'm scared to drive my car, don't want it to turn
off. What can it be? Not sure what to do. Help