The last few times I've driven my Dart, I've noticed a weird sound almost sounds like a vacuum leak, seems to be more pronounced when hot. I have not checked for vacuum leaks but the car runs fine other than the noise, until today.

Today as I got home, turned the car off, went around to open the garage then came out and started it, it was hot (216 water temp) and once I got it in the garage I turned the fans on, and after about a minute of running, it died.

I was watching it as it ran and I could see (I have one of those plastic see thru fuel filters) that within the filter there were some bubbles (not a rolling boil, just a few bubbles) and the filter -- which is mounted so the fuel goes vertically up -- was only about 50% full. Once the car died I verified that the fuel level in the carb was low because I have the see through fuel level windows.

So there is some problem with the fuel pump I think, not pushing enough into the filter (I have looked at the filter in the past and it's full). Would it also explain the weird vacuum/whirring sound? The fuel pump is about 5 years old, it's a carter mechanical stock replacement.

So could the fuel pump issue and the noise be connected?

Generally fuel pumps only need to be replaced because they get a hole in the rubber diaphram and begin to leak. They have a hole in them for this fuel to come out of, like a water pump.

I don't think I've ever seen a stock mech pump keep one of those filters completely full, especially vertically.
When mine have gone bad, there's no sound at all: the motor quits running!

Hmm well I know I've seen it before, full of fuel. If that's not normal for most pumps, it was for this one.

Today it caught my eye because of those bubbles and not being full, but around 1/2 full and moving around, with bubbles.

The carb was not getting enough fuel to the bowls keep the car running. The usual level is mid-way to the center of the glass sight window, and both were below the windows. Maybe I'm answering part of my own question here, but I think there is something wrong with this fuel pump. Im thinking if it was a needle/seat issue, it would not affect both bowls simultaneously.

Unless someting else comes up I'm going to plan on switching to an electric pump and we'll see how that works and if the noise goes away.

you sure you dont have a leak between the tank and the pump? if you hear a sucking sound, and you see bubbles in the fuel, coming out of the inlet, you might be sucking air close to the pump.

I will look for leaks, thanks.

Does the filter fill when the car is first started and the problem occurs as it heats up?

Every time I have had a mechanical fuel pump go bad I could always tell by the engine losing power under wide open throttle as soon as I hit second gear. It seems the float bowls had just enough fuel in them to get it through first gear before the pump couldn’t keep up. Let up on the go peddle and the engine would pick up again. Take it out and run it out in first gear if it noses over about the time you grab second gear you have a bad pump. I never had one make noise that I could hear over the exhaust.