Just wondering if why Black plays 7...c6 instead of 7...Bb7 followed by 8...c5 then the c4 break will be refuted by 9.c4 b4! and White has a backward pawn on b3

Hey Helltank, Nice PAWN you have there on c8!  Analysis has been done before in beginner Ruy Lopez books on what White should do if Black is stupid enough to force the ceding of the Light-Squared Bishop.  You play like that as Black, you'll lose if you play anybody worth anything!

"RL Refuted" refuted (by me).
What if 4.Bxc6, it's well-known drawn position. Ha! :)

I put the position after Nxb3 straight into chessmaster 10 for a 10 second analysis.

The Chessmaster recommends: Pawn at a2 takes knight.

Analysis: Your pawn at a2 takes knight, which removes the threat on your rook at a1. Black replies by moving pawn to d5, which attacks your pawn at e4. You move your pawn to d3, which protects your pawn at e4. Black responds with pawn takes pawn, which attacks your knight at f3. Your pawn takes pawn, which removes the threat on your knight at f3. Black responds by moving the bishop to d6, which removes the threat on Black's pawn at e5. You move your knight to c3. Black counters by moving the bishop to b7. You move your bishop to e3. Black responds with the knight to f6, which clears the way for a kingside castle.

As a result of this line of play, you win a knight and a pawn for a pawn. In addition, your mobility is greatly increased. Also, Black's pawn formation is somewhat disrupted. Finally, the pressure on Black's King is slightly increased.