Regarding the pump out during fill when a cycle is started from the get-go ... you have either a bad diverter valve, or it's not connected properly after the son disassembled/reassembled the machine. The valve controls which direction water flows when the pump runs -- either out the drain hose (diverter off) or back into the tub through the recirculation port at upper right/rear of the tub cover (diverter on).

All cycles except Perm Press start with what F&P calls EcoActive wash. A small amount of water (at the selected temperature) is run in to saturate the clothes and dissolve the detergent. The diverter valve is activated and the pump turns on to shower the concentrated detergent solution over the clothes for 3 to 5 mins (while the basket rotates at 25 RPM). A bit more water may fill to top-off the required level for keeping the pump primed. After the recirculation period, the machine fills rest of the way (to either an auto-sensed water level or a manual-selected water level) with COLD water for an agitated wash.

Your diverter is not functioning, thus when the pump turns on for EcoActive recirculation, water drains instead of recirculates.

As per your 4th paragraph above, if a cycle is started with the tub already filled beyond the very low EcoActive water level, it'll skip that function and go on to the agitated wash. Perm Press also skips EcoActive by design, goes directly to the agitated wash.

The diverter valve can be operated in Diagnostic mode via the Delicate cycle button (this info is not on the Tech Sheet you may have found in the console). The diverter is a wax motor, takes a couple mins or so to shift into recirculate when activated, 3 mins or so to shift back to drain when deactivated. There's no indication on the console when it shifts, you just have to turn the diverter on or off and wait the requisite time before turning the pump on.

Delicate (diverter) On + Regular (pump) On = recirculation

Delicate Off + Pump On = drain

Source: Fisher Paykel GWL11 washer: starts pumping out before full