New Zealand appears to have achieved (2).
For example, many countries kept mandatory smallpox vaccinations long after the disease was eradicated within their borders because otherwise a single traveler can wreak havoc. Check for example smallpox reintroduction to Yugoslavia in 1972 by a single pilgrim. A quick martial law and quarantines helped contain it, but even then it caused, according to Wikipedia, 175 infections and 35 deaths.
If COVID-19 is as virulent as it is claimed to be I would not bet on NZ staying COVID-free after travel restarts. My 2c.