Your fuel system is pressurized...you should hear a "woosh" sound when you unscrew the gas cap. This will be more noticeable on hot days, when the expansion pressure is greater.
As far as your noisy fuel pump...not related. But how noisy is the pump is a subjective question. You SHOULD hear the pump operating, but it's more of a hiss than a buzz.
A buzzing pump generally means it's wearing out, although many members here have buzzing fuel pumps that operate normally.
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car