The oil pump should be directly driven inside the engine. If the engine is running, the oil should be pumping. If the oil pump was not working, the engine would not have run "seven to ten minutes".
What you are probably hearing is all the internal engine damage done when the old pump quit. At the very least, you need a set of crank and rod bearings. The noise lessens when the engine warms up and rod knock/piston slap is taken up by the heat expanded parts.
Did the shop recommend any additional work when you brought them the vehicle with the bad oil pump?
Did they replace the oil and filter when they did the oil pump? If so, they should have used a quality filter with a check valve, not recommend that you get one now.
The sending unit may be just fine, but the ruined bearings are leaking oil pressure and not allowing a proper pressure to build.
It's tough to call without seeing/hearing the vehicle, but I think I called it right.
Anyone else?
(edited fer spellin'!)