Chess on an Infinite Plane (hitthepin - vickalan)

Yes, playing me. But I hope PixelbyPixel will find someone to play (if he wants to).
My move:
1...(3,5)

I actually hope that this game does not get analyzed by computers soon. It's fun to play games where only "humans" have analyzed them so far.
My move:
2...(5,6)

Can the 1, -1 white pawn double move on its first move. Additionally can it double move on its second move if it moves to 2, -1?

hitthepin
@neoliminal: all pawns are the same as normal pawns. Any pawn can make an initial move of 2 squares, and the initial position does not matter.
My move:
3..(3,5)x(4,4)

And theoretically this would be a legal sequence for White? :
Q(4,1)(0,-3)
Q(0,-3)(-11,7)
Q(-11,7)x(-4,15)

White can attack the (-4,15) pawn like this:
Q(0,-3)
Q(-11,8)
Qx(-4,15)
(You almost had it correct).
Also, friedmelon made some interesting queen moves like Q(5,999)+. You can see it in post #11 (in this game).
Btw, please don't talk about possible moves too much here because it could help one of us. But questions in general can be asked (here).
This thread is a game of "Chess on an Infinite Plane" between hitthepin and vickalan
Rules:
The Pieces:
Black and White each have the following pieces (quantity and name):
1 king
1 queen
2 chancellors
2 rooks
2 bishops
2 knights
2 guards
2 hawks
24 pawns
All pieces move as in classical chess, with the "extra" three pieces moving as follows:
Chancellor (C) - Moves and captures as rook + knight.
Hawk (H) - Leaps exactly 2 or 3 squares in any orthogonal or diagonal direction. The leaping move means it can jump over other pieces.
Guard (G) - Moves and captures the same as a king but is not affected by check.
Pawns play the same and promote at the same rank as in classical chess. White pawns promote at rank 8, and black pawns promote at rank 1. Pawns can promote to chancellor, hawk, or guard in addition to queen, rook, bishop, or knight. Pawns may capture and be captured en passant with the same rules as in classical chess.
Board Setup:

A red bracket indicates the a1 (1,1) square.
There is no castling.
There is no fifty-move rule. Draws can only occur from stalemate, threefold repetition, agreement, or a proven case of insufficient material to force checkmate.
All other rules are the same as in classical chess.
Move Notation:
Numeric coordinates are used to identify piece locations as (file#, rank#). Parenthesis are used around each coordinate. Three examples of a move notation:
1) A rook moving from (8,4) to (1,4):
R(8,4)-(1,4) or R(1,4)
2) A rook moving from (1,4) and capturing a piece on (0,4):
R(1,4)x(0,4) or Rx(0,4)
3) A pawn advancing from (-1,7) to (-1,6):
(-1,7)-(-1,6) or (-1,6)
hitthepin plays White. Good luck!