Aviation Formulary V1.44 is helpful for formulae.
There are two reasons why altitude is important to aircraft:
A) Avoiding terrain and obstacles
B) Avoiding other aircraft
For B, which is what ATC is involved in, you can use any datum you like, provided all the aircraft that are being separated from each other are using the same datum. So ATC would much prefer to use flight levels all the time -- it's those damned aircraft that insist on using a datum that approximates to true altitude at lower levels (for purpose A).
That should give you a clue to help with "Is it based on the pressure at the aircraft position or the ATC location?"
"And does the altitude of the aircraft change the 28mb/ft bit of the formula?" takes a bit more thought to get your head around. If you imagine the atmosphere stratified into flight levels, then consider what happens if sea level happens to be offset from FL000, you'll notice that the difference in level between e.g. FL350 and 35,000 ft is the same as the difference between FL001 and 100 ft, or FL000 and sea level. So while the 28 ft/mbar bit will vary ever so slightly depending on the QNH, the altitude of the aircraft makes no difference to the correction applied.