No Qantas don't fly there anymore - they codeshare on Air Tahiti Nui (A340) and Polynesian (738) from Auckland.
Most flights do arrive at night.
To add to your list of airlines, you have of course Air France with 744s, Polynesian with 738s (with winglets too!) and Lan Chile 2-3x a week with 763s.
PPT also has a lot of charters. When we were leaving there on a Lan Chile flight to Easter Island there were no less than 3 (!) HA DC-10s at the airport. Two were operating charters to LAX and the other was grounded after doing a dive into the bay at the end of the runway!
As for spotting. The view from the terminal itself is non-existant. However i would imagine good views are to be had from elsewhere.
Good luck, because there seems to be only 3 pics of PPT on the database...
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Photo © Alexander Ananian-Cooper