How many moves out do the static board evaluations use? These days many online chess websites offer a board evaluation rating, often a bar, sometimes a number, sometimes both, as is the case here (see two red circles):

Black will take a pawn soon, so the evaluation is -0.9 pawns to white.  Note that there are two components to the score.  First, there's a raw score due to some sort of piece scoring system.  Second, there's a positional evaluation scoring element that considers future moves and future pieces that might be taken.  Seems clear, right? 

Not exactly.  Consider, near the end of the game, a pawn can get converted into a queen.  Using the most popular piece-ranking systems, a pawn=1 can switch to a queen=~9 via this process.  Therefore, if a player is a pawn ahead, and players play well, eventually, on average, one can expect that this might get promoted to a queen.  Perhaps if you averaged it would be 3 (wild guess) considering that most other pieces can't get promoted.  Anyway, one can see that the second term in the ranking scoring system has a look-ahead variability in that lopsidedness will increase in positive feedback fashion such that a 1 is much higher the further an engine looks ahead.  This positive feedback would exist even without promotions.

My question is just how many moves these engine look ahead in ranking static boards.
Note that there are two components to the score. First, there's a raw
  score due to some sort of piece scoring system. Second, there's a
  positional evaluation scoring element that considers future moves and
  future pieces that might be taken.


This is wrong. The "piece scoring system" is part of the positional evaluation that is considered at the end of possible lines. It doesn't matter what the pieces are now, it matters what they will be in the future. Therefore the -0.9 is equal to the score after the best move black can currently do, 2...dxe4. It's also equal to the score after the best move white can answer to that, moves other than 3.d3 apparently scored worse. This is called the "minimax algorithm".

At the time static evaluation is done, it looks only at that exact position and doesn't look ahead more moves. The looking ahead part is done by then.

Pawns get different scores depending on where they are. I think that most engines compute some score that says how "endgameish" a given position is, and if it's more endgameish then a pawn gets a bigger bonus for being far advanced, but that's actually guesswork on my part.