As pilots are taught at CPL level that they can perform a daily inspection on the Piper Warrior they are flying, many assume that means they can "daily" any aircraft.
In fact, that authority stems from
Civil Aviation Regulation 42ZC, and is only for Class B aircraft, as specified in Schedule 8 of the CARs.
For transport category aircraft (Class A),
the daily can not generally be performed by an endorsed pilot (i.e. without SPECIFIC authorisation) - it must be completed by an engineer under the schedule of maintenance.
So to answer the original question:
I have never seen or maybe miss seeing if the PIC checks the quality of fuel, via each tank draining point either first flight of the day and/or after each refueling. As the PIC has the sole responsibility, can he or she delegate this responsibility to another crew member to whom ever does the walk around?
The pilot doesn't do the daily, which the fuel checks are part of, because a pilot on a Class A aircraft
is not permitted to. It's the engineer's job, and the only requirement for the pilot is to check that the daily inspection certificate has been signed for that day (by the engineer) before operating the aircraft.