The buzzing fuel pump is not good at all - you're going to have to replace that very soon, whether it's the current problem or not. It can be done by a noob, but it's a huge pain. To give you an idea about non-Q45 techs and repairs, I had Nissan techs do my pump and they STILL managed to bend the sender float and had to go back and fix it. Here's an extremely detailed, step by step writeup for a fuel pump R&R, from the archives:
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You can fairly easily pull the FPCU and check it for signs of overheating. Do that right away. The FPCU can fail intermittantly after having been overheated by an aging fuel pump. If there are no signs of burnt connector pins or solder joints, then neither the FPCU nor the pump are probably your current problem.
FSM is Factory Service Manual, TSB is Technical Service Bulletin.
Don't be afraid to become familar with this forum's search function. Almost everything imagineable has already been diagnosed and dealt with at some time in the past 4 years of archived threads.