Is this case considered an ambiguity or not? From the answer to my question How are PGN ambiguities handled?:


  In the case of ambiguities (multiple pieces of the same type moving to
  the same square), the first appropriate disambiguating step of the
  three following steps is taken: ...


After reading that, a new ambiguity surged from that disambiguation, it is not clear what would happen if the pieces that look like they can move to a same square are all pinned except one piece, is then a need to disambiguate even if only one of those pieces can legally move in there?

Here is an illustrated example:

[FEN "4k3/8/8/8/8/8/8/q2NKN2 w - - 0 1"]


Should I use Ne3 or Nfe3?
While it's not ambiguous (only Nfe3 is legal), it is better to be specific with Nfe3.  Successful software can deal with both Ne3 and Nfe3, but not every pgn parser is perfect, and some beginners will appreciate the additional guidance.