Under what conditions can I cast Panglacial Wurm from my Library when my opponent controls an Aven Mindcensor?
It is option 2, you can cast Panglacial Wurm if it is in the top 4 cards.


  701.18f If searching a zone is replaced with searching a portion of that zone, any other instructions that refer to searching the zone still apply. [...]


Because Aven Mindcensor uses the word "search" in the replacement, it is still searching. It is just now searching a sub-set of your library.

The regular event of searching your library never happens in this case, so a Wurm somewhere else in your library won't do anything:


  614.6 If an event is replaced, it never happens. A modified event occurs instead, which may in turn trigger abilities. Note that the modified event may contain instructions that can’t be carried out, in which case the impossible instruction is simply ignored.


The reason number 3 doesn't work is that you don't have the Wurm available to cast. If you aren't seeing it while searching, you have no way of "knowing" that it is even in your library. You wouldn't be allowed to rely on having your deck list memorized to know that. And even if you do know for sure that it's in there, you aren't allowed to search the rest of your library to find it in order to cast it.

This was addressed and confirmed by a judge here.