(oops, after posting I see you're almost 1600 in daily, this answer is probably a little confusing, sorry about that. Learning openings 10+ moves deep is probably not the most important thing you could be doing right now)
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As a brief intro let's look at:
11...Bd6 12.Qa5.
Obviously Qxa7 is a big threat, so how will you defend it? 12...Kb8 loses a piece right away, and 12...a6 gives white the important b5 pawn break eventually. I hope you can understand that much without any other comment because the rest is a bit harder.
Before that though, I will say the engine backs you up that 13...f6 and 14. Qg3 are inaccurate. It says white should play 14.Qa5 and so black should play 13...Bd5. However there are a handful of GM games and none of them played this way, so it's useful to understand why. Here's what I think.
First let's look at the queen going to the queenside like you said:
13.bxc3 f6 14.Qa5 a6
Previously a6 was undesirable for black because of the b5 break, but now white has no b pawn. Meanwhile black has the idea of Bd5 + Qc6 which will force a pawn in front of white's king to move. So White may have thought the queen is off sides on a5. Both the opposite side castling and opposite color bishops point to the possibility of dangerous attacks on both kings, so white would rather the queen stay in contact with the kingside for defense, and judging Qa5 ineffective, would rather stay in contact with c7 for offense.
Second let's look at the queen not going to the queenside
13.bxc3 f6 14.Qg3
Now Bd5 + Qc6 doesn't force a pawn to move. For white's attack, let's imagine a setup like Qg3, Bf4, and Re1-e7... if at any time black's c pawn moves then suddenly sequences like d5 plus Bxa7 completely undermine the squares around black's king. For example b6 would no longer guard against an attack on the b file.
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This thinking by White turns out to be incorrect, because as black advances the pawns, the queen simply gets in the way and gives black tempo.
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Full game here https://www.chessgames.com/perl/chessgame?gid=1068203
So lastly let's see what the engine recommends
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Conclusion
So yes, both 13...f6 and 14.Qg3 are inaccurate.
This is a sharp position due to opposite side castling and opposite color bishops. One tempo can be the difference between winning and losing, and you see you have to be concrete, and that even GMs misjudge how to play.
I'm learning my first opening for Black and I was hoping someone could help me understand the move 11...Bb4. Opening Databases have it and the computer recommends it. Supposedly it is to guard against Qa5, but black promptly trades away this "defender" and White seems runs the Queen away as if they were never aware of the Qa5 idea. Black's move and White's reply seems so pointless.