En Passant can only be played when the enemy pawn moves over your pawn's capture square during it's first move (moving 2 squares); so the answer to both condition 1 and 2 is no.
It is not possible for a pawn to en passant twice in a row.
My understanding is in early chess pawns could only move one space at a time, so when the 2 move rules was added they also added en passant to counterbalance the fact that you might lose a chance at capturing your opponents pawn since he could now move over your capture square.
So, in essence, because after capturing en passant it is no longer possible for an enemy pawn to pass over your capture square, it is no longer possible for your pawn to capture en passant.
The official FIDE rules, article 1 section 3.7d states:
A pawn attacking a square crossed by an opponent’s pawn which
has advanced two squares in one move from its original square may
capture this opponent’s pawn as though the latter had been moved only
one square. This capture is only legal on the move following this
advance and is called an ‘en passant’ capture.