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Can there be two bishops on White squares? If not, can my queen be captured and then be promoted so I can win the game?

I reallly. don't know what to do because I think you cannot that have two bishops on White squares when the bishop is the only captured piece.

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    The position shown is simply not legal. It seems you think a pawn can only promote to a piece that has already been captured. This is not true; in fact, a pawn can promote to any piece (except kings and you might need to borrow from a different chess set), and this has to happen the moment you move a pawn from the 7th to the 8th rank. Because of this, you can never have a pawn just standing at the other end of the board. – 11684 Jan 8 '17 at 22:16
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    @11684 The position is legal: 1.e4 e6 2.d4 c5 3.d5 Nh6 4.Bxh6 gxh6 5.Nf3 b6 6.Bc4 Bb7 7.Bb3 Ba6 8.dxe6 Be7 9.Qxd7+ Kf8 10.exf7 Rg8 11.fxg8. Some of the moves were bad, but no rules were broken. – bof Jan 9 '17 at 7:35
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    @bof A pawn on the eighth rank is simply impossible. It has to have promoted by then. Tony Ennis' retrograde analysis comment explains this better. – 11684 Jan 9 '17 at 7:39
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    This is based on my assumption that the OP has had the pawn there for at least a move. Since he considers first sacrificing the queen to be able to promote the pawn, it seems he at least thinks having an unpromoted pawn on the eighth rank is legal. – 11684 Jan 9 '17 at 7:42
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    @11684 The physical procedure for promoting the pawn would be: (1) remove the black piece from g8; (2) remove the white pawn from f7 and put it on g8; (3) replace the white pawn with its promotion piece. Clearly the photograph was taken partway through white's move; White has captured a black rook with his pawn and is asking us what he can promote it to. – bof Jan 9 '17 at 7:59
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Your only problem here is logistical. You can promote your pawn to any piece except the King, even if that means you have two bishops on the same colour squares, or two (or more) queens on the board; but according to the official rules, you must replace it physically with a piece of the correct shape and colour. What to do if no such piece is to hand?

In a tournament, the organisers will make sure to have spare pieces available for such contingencies; but in a home game, improvisation is the norm. For instance, if one of your Rooks has been captured, you can turn it upside down and call it a Queen. In this case, you can just say "that pawn is now a Queen", which ends the game immediately with checkmate.

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    Great answer. People might wonder why on earth the rules say the promoted piece has to be the same colour. Why on earth would you want to give the opponent an extra piece? Well, suppose that black has king on f8 (as above), rooks on e8 and g8, pawns on e7 and g7 and white has pawn on f7 and rook on f1, king somewhere not involved with the action. Black is completely winning unless white can capture one of the rooks and promote to another black rook. Some similar position must have occurred and been complained about to trigger the addition of the extra condition. – Brian Towers Jan 9 '17 at 11:51
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    I forgot to mention. "What to do if no such piece is to hand?" In an official tournament you should stop the clocks, call the arbiter and ask for the piece you want. You don't have to lose time on the clock hunting for the piece yourself. – Brian Towers Jan 9 '17 at 11:55
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    @BrianTowers You can read how the extra condition was added to the rules here, along with the condition that it has to promote and can't stay a pawn: en.wikipedia.org/wiki/… – tobiasvl Jan 11 '17 at 21:27
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11684's comment is correct. You can have 2 White bishops if you want. It is possible for you to have 9 Queens, if you want. You can't have:

  1. A king
  2. A pawn
  3. Per Brian, a piece of your opponent's color
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Good answers here already, but I don't feel like they actually answer the question(s).

Can there be two bishops on white tiles?

Yes, there can. You can promote your pawn on g8 to a Bishop. Luckily you can use the dark-squared Bishop that has been captured, ready at hand at the top of your photo, for this.

Tony Ennis has summed up the only restrictions on promotion in his answer. If you still had both Bishops on the board, TonyK's answer explains how to deal with that logistically, so even in that case you could've had one dark-squared Bishop and two light-squared Bishops on the board.

If not can I get my queen killed and change my pawn to a queen and win the game

This question has two parts/misconceptions, I believe.

First of all, you need to promote the pawn immediately as it reaches the eighth rank. As soon as it set foot on g8, it must be promoted before your turn ends, and it can't stay a pawn on g8. Therefore, you can't get your Queen captured/"killed" and then promote your pawn afterwards.

Secondly, just like you can have two light-squared Bishops on the board, you can also have two Queens on the board. If I understand you correctly, you're proposing that you sacrifice your Queen in order to be able to promote the pawn to a new Queen. This is not necessary; you can just promote to a second Queen right away. Again, like TonyK said, the only problem with that is logistics: If you don't have a second Queen piece at hand, stop the clock and look for one, or use an upturned Rook, or something else. Seeing as promoting to a Queen there immediately wins the game by mate, however, it's probably not necessary to do that.

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