1. I understand that I can collect QF points on LATAM flights.

Correct, but no status credits unless you are on a QF codeshare.

2. Does LATAM recognize QF status (for example on boarding passes)?

No, my recent boarding passes just noted that the FF program was Qantas. As Qantas Gold, all my boarding groups were general ones after business and LATAM priority groups had boarded, seat allocations indicated that I did not have status in LATAM's eyes.

3. If so, when flying an international LATAM flight does QF Gold status qualify for entry to a LATAM departure lounge in SCL (or anywhere else, e.g. MIA)?

Only if travelling on a QF codeshare. At the GRU lounge I had to show my boarding pass which scanned to show the codeshare. I did not try at other ports because flight delays meant tight connection times didn't allow time to attempt a lounge visit.

If you have a Delta account, it might be better to credit there as LATAM flights count towards status with them