To me, this game seems like it is all about cutting and connecting. The player who does this better is the one that will win. I am only about 2-3k, so perhaps my analysis is inaccurate, but I'll give my thoughts anyway.

- This move looks horrible. Aji keshi to an extreme level. Why black chose to peep this cut so early, I don't know. Yes, he gets a "wall" toward his enclosure, but that wall does not secure him points. Instead, it simply makes white locally alive and strong.

- This seems like very poor direction of play. O3 is low and white's strong group above the corner will prevent black from building anything substantial on the bottom. It is also inconsistent. Black said with his little wall that he wanted to build toward the top. Why did he not approach at F17?

- You are correct. The cut is the only move I can see here. Also, as a follow up, why not press black at R11 and jump to P10? It better surrounds black's stones and leaves more aji against black's upper right.

- This is the right idea. Black is keeping you disconnected.

- This move seems odd. Why not jump to P13? I understand that you don't want R10 to be an eye, but if black takes gote to make that an eye now you can play some nice reduction/settling moves like S16 because your group is out.

- It is good that your goal was to keep black separated. But don't forget what is important here. The white stone at R14 is doing an amazing job of reducing black. If you are going to sacrifice it, you must get just compensation.

- I think saving at Q12 is bigger than following up on your threat. Once black has that ponnuki all hope of reduction/invasion in the upper right is lost.

- This seems like a fine move. You are splitting black in half on the bottom and black's only choice is to connect on top with M4 and allow you to fight for life there.

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No. Absolutely not. Your opponent needs to read "Lessons in the Fundamentals of Go" Chapter 2. This move should almost never be used and this is not a situation to use it. After you extend to N4 his corner is in serious trouble.

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Why? You are keeping your stones behind enemy lines. Your white group at P6 is very strong. Standing up here all but connects you to it and then you can go to town with moves like S3, J3, K5, or any number of interesting follow ups. What is the follow up to this? A hane at O4 that black would need to be mental to allow you to have?

- Thank goodness one of you played a reasonable move here. Now black's corner is much stronger and white's stones are in jeopardy. Creative moves are not required in basic situations like this. Keep your stones connected, stay strong, and don't let your opponent take vital shape points.

- Alas, this move comes too late. Black will not allow you to connect anymore.

- I think the only option now is to sacrifice the white stones. Leave that position and move on. C9 is a large move at this point. L15 is also important to help against top-side invasions.

- If black connects solidly here, I don't see how this will ever end well for white. The group has no eye potiential and nowhere to run. Yet white has made it heavy. If black stays strong, white will be forced to run for the next 30 moves. Not a fun game.