1990 740 Turbo, buzzing fuel pump

assuming it's about the same as the fuel system on my '89 240, I'd say your mechanic is probably right! If the in-tank pump fails to deliver fuel to the other pump, it has to work harder. Another source of failure is the rubber coupling between the in-tank pump and the outflow line. However, if you have to pull the pump out, you might as well replace both at the same time! Until then, I've read that keeping the tank more than half-full helps.....

Very common, and probably correct diagnosis. If the delivery to the main pump is choked, then the fuel may cavitate in the line to the pump input. The pump pumping this vapour-liquid is the noise you hear.

Make sure your primary pump "the one in the tank is working "as it overload the main pump which has to pull too hard . If your mileage is up high may be better to replace both and bite the bullet as most times the strain ruins one or both pumps as well the fuses to the pumps melt the connections .