interactive lichess analysis board

I'm still pretty new to chess notation, but I'm not sure the solution is accurate. Or maybe I'm misunderstanding.

Yes, it is not forced checkmate in a few moves, but black will lose their queen and white will just end with an extra bishop versus King and pawns. The resulting endgame position should be pretty trivial to win by just eating some pawns with the bishop and then promoting one of your own.

Chess puzzles don't always end in checkmate, often it is enough to just win a piece and gain a clear advantage. The phrase "... to move and win" is a little confusing tho, you're right

How do you know when you're done? The solution is 3.5 turns, why not 4? 2.5? This seems unnecessarily arbitrary

And... Black doesn't lose their queen?

Good question, when doing puzzles on lichess.org or chess.com or other platforms you'll just have to keep going until it says you're done. Sometimes it can feel a little arbitrary, but usually it's the end of a forced sequence of moves. Here I just did not bother to keep going, because again it is now trivial and the "puzzley" part is over after you take back the queen and are up a piece.

What do you mean black does not lose the queen? Either black takes the rook on e6 and it gets recaptured with the bishop or the king moves up like in your screenshot and white takes the queen with the rook and is now up two pieces even.