then black loses a bishop with no compensation, or black loses a rook for a bishop. Both favor white. 

But the rook isn't toast.. after Nxc6 Bxc6 Rb8 Bxa4.. it's not up a bishop, but some material and an advantage. So black has to move the queen to prevent this..

By the way, the second variation is a bit sneakier but it might favor black. I would personally play d4 directly, and not try the d3 to d4 set-up losing a tempo. It's good to know, but just glancing at it looks like it gives black a chance to keep it even.

9...Nd5 would also save the rook. But that just seems awkward for black. This position is well known and tons of articles/coverage...my main focus was the move order/lines. It leave whites with alot of options, especially against Indian defense. I also like that white can employ 1. d4 attacks, without the worry of Nimzo-Indian which is very commonly employed by black. 

If 9...bxa4, or ANY move other than a queen move, black will lose the bishop. if 9...bxa4 then 10. Nxc6 Nxc6 11. Bxc6. White recovers the pawn, and the a8 rook is toast. Plus the doubled isolated pawns, and a pawn hanging on a4. it would take exceptional play for black to recover. 

I know in queen and kings gambit it is usually bad for black to protect the pawn after accepting, or probably in most cases. Id rather be white in this position, and I think the continuation is something like 9. .. bxa4 10. Qxa4 Bb7 11. Then is Ndc4 or Nec4 better here? Or are both just decent options? Or bad..