1. What are possible symptoms of a fuel pump dying?

I've had this problem for the last couple of years where the car wouldn't start after I'd parked it for a few minutes, just cranks with no sign of life. What I've done is pull the fuel pump fuse, look at it to see it's okay, put it back and it would start okay. Today was different. I was stopped at a traffic light when it died and wouldn't start. The fuse trick didn't work. A guy helped me push the car around the corner into a driveway. I was telling him about pulling the fuse and showed him, and lo and behold, it started! It died again and wouldn't start, but then I switched some more fuses and it started. I drove to where I was going, to get the car oil sprayed and then it wouldn't start and they had to push it on the hoist. It started for me when I left, but immediately stalled as soon as I got out on the street. Played with the fuse again and got it going and it ran okay all the way home, about 10 minutes. So, does this look like a bad fuel pump, or could it be something else, FI relay?

2. I'll be ordering a fuel pump anyway. Are there any other bits I need to order to do the job?
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1992 745 approaching 500k km