Haven't looked at the second two much yet, but the first one is wrong. Black has the advantage if he plays correctly against 6.f4?!
Tactical Motifs -- Sicilian Defense

Instead of 9...fxe6, 9...Bxb5 is better even if it gives up the castling rights. Pretty much an equal game but kinda unbalanced since both kings are open. Then again, why play Bg7 when there's 6...Nc6 which leads to a less complex game. The Levenfish isn't as aggressive as it looks but it's a good surprise alternative to the Yugoslav Attack.

The first example is indeed wrong. White should recapture on d1 with the King, not with the c3-Knight.

The first example is indeed wrong. White should recapture on d1 with the King, not with the c3-Knight.
good calculation @blueemu
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I've always tended to think about chess in a "tactical" sort of way. I find that learning new tactical motifs helps tremendously, so I figured I would post a few here that I thought were interesting and similar.
Full disclosure: these lines are not my original ideas. Credit for the first line goes to GJ chess, and his youtube channel, the second line is from Mayhem in the Morra by Marc Esserman, and the credit for the third line goes to the infamous Chess Assassin, Bobby Fischer, RIP.
Comment and Enjoy!