This seems to be a common problem but it doesn't necessarily mean it is the fuel pump but the sender wouldn't be the cause. It could be a number of things, the one that seems to be the most common is the CAS (Crank Angle Sensor).
Check for any error codes. Do a search on how to do that, I don't have time to search for the link at the moment.
The sender is for the fuel gauge. It "sends" the fuel gauge the fuel level reading in the tank. If the sender stuffs up, it wont make the car stall or randomly cut out, it will just stop the fuel gauge from working. The stalling/cutting out will most likely be a problem with the fuel pump itself, thats if it turns out to be a fuel related problem thats causing the stalling etc...
if u are going to do the pump u may as well do the whole pump module so then u know its all good, only costs a little more and will save u getting it all back together and realising the sender is faulty aswell, 13 years on a wearing part most at that age will be worn out and alot of people dont realise because the gauge reads fuller when its playing up...