I'm probably out of my depth here, but don't pilots use QFE at low altitudes to set the altimeter, so that their altimeter reads zero when on the deck.
Yes, that's precisely the purpose of QFE.
Or do pilots always use 1013.2 to set their altimeter, even at low altitudes?
1013.2 is the setting that Flight Levels are based on, so it's normally only set above the transition altitude (unless of course the QNH on the day happens to be this value).
And is this the same altitude transmitted on ModeS/ADS/B?
The altitude transmitted on Mode S/ADS-B is always based on 1013.2 and not on the altimeter setting, so above the transition altitude it will be equal to the Flight Level. Below the TA it won't be a true altitude AMSL unless the QNH also happens to be 1013.2
Which is where we came in ...
Surely most aircraft can't determine an aititude without the pilot entering an air pressure?
Quite so - they can determine what Flight Level they are at, but not what altitude.