car stalling

Your mechanic friend is 100% right; there are check valves at the inlet and at the outlet. Sounds like both are stuck open for the fuel to be sucked back. (In particular, you can test the outlet vavle with it hooked to the carb; pressure ought to stay in the line between the pump outlet for quite a while after the engine stops turning if the needle valve and outlet valve are good.)

And possibly the pump diaphragm is busted and the fuel is draining back into the crankcase. Probably not, but smell the oil on the dipstick to be sure it does not smell like gas.

BTW with the pump output line into an open container, it ought to pump out a pint or more in about 45-60 seconds at cranking speeds. Most can do this and more.

Either way, replace the pump. It could be a faulty pump. Also, you could have crud in the fuel tank that was sucked into the pump and is mucking up the inlet and outlet valves. You might want to put a clear filter inline before the pump for a while and see if it accumulates some crud; if you do have crud in the tank, it may clog this filter but at least you won't mess up the new pump.

Blow by mouth back into the main line to the tank with the gas cap off. It wil have some resistance, but you ought to be able to blow back into the tank. A lot of back pressure indicates the sock is plugging up and you have crud in the tank. Nothing to do at that point except pull the ank and inspect and clean and replace/recoat inside if you find a rust.