Where exactly does Oyster need to be touched? Just at the start and
end of the journeys, or also at the NR Oyster validators by the sides
of their platforms? What about if I get on at a tube-only station, get
off at a National Rail-only station? Where should Oyster be waved
then?

With a travelcard, you need to have touched in at least once and
touched out at least once at stations where prepay is valid, so you
wouldn't need to use the validators at Northolt or Ealing Broadway.
However, you would need to use one of them if you were going to (for
example) Drayton Green.