Weird puzzle thread

I already opened a similar thread on the general lichess forum but IMHO it's much more appropriate here, in the group of puzzle aficionados. If you chanced upon a puzzle where the solution baffles you, bring it here and let's discuss it.
I will start by this: lichess.org/training/bG793
I don't understand why Black plays Bg5 killing its own bishop without any retaliation, instead of Bg7 which would also attack the White queen but this time from a protected square. Any ideas here?

@margaritaor Because Stockfish prefers White to have a big plus score rather than Black to be checkmated. If 14... Bg7 then 15.Qxh7#.

Gosh, how could I have overlooked that... Thanks!

By the way, after 14...Bg5 15.Qxg5, Black is in *big* trouble. Stockfish plays 15... e6. Now you have a new puzzle! White wins. You'll be amused at Stockfish's play as Black.

Now you gave me a difficult puzzle! I also don't understand that ... e6 move:( After that I just reverted to the previous mating threat with 16. Qh7 and saw Stockfish play 16. ...Qg5. losing their queen. But I don't see immediate checkmate after that.

Another weird puzzle here : lichess.org/training/ZSuII,

My first idea was that 1. ...Bxd3, 2. Rxd3, Rxd3 trades a rook for a bishop and thus wins the exchange. This is apparently wrong: the correct solution per Stockfish is ... Rxd3, 2. Rxd3, Bxd3 3. Kb1, Qxc2+. Now, Qxc2+ is not a checkmate because the king can escape to a1 and the first rank is guarded by a rook. Why is this better than 1. ...Bxd3, 2. Rxd3, Rxd3?

@margaritaor
Do you know how to use the interface for Stockfish in the browser? Or are you using the app? In the browser, you can turn on Stockfish after the puzzle has ended and try various things. For example in the puzzle in post #1, after 15.Qxg5, press the threat button and you will see that White is threatening mate in 4 moves. Turn threat off and you'll see the moves Stockfish is looking at and the score for each. Stockfish comes to the conclusion that Black is losing regardless and that 15...e6 gives White the lowest positive score of the various Black alternatives (+13.3). So Black is still losing, and gives up the Queen to stop mate. After that, White is threatening mate in 2. White has no immediate forced mate.

On the second puzzle, see if you can fire up Stockfish to see why 1... Bxd3 is incorrect.

Answer: Because White plays 2.Rd2 not 2.Rxd3 and the score is +0.3.