[ТУРНИР-HotA] Diamond: Survival

By the way, regarding analyzing the options, what do we do if, after our Kxf7, Black pushes the rook to g3? If we respond by pushing the rook to d8, then a check with the queen on f2 follows, and checkmate with the bishop on g2. Or am I mistaken?

There's no need to push the rook to d8; it doesn't hinder anything. Instead, we should capture the pawn on h6 with the knight, giving check. The black king escapes to f8, and then we capture the bishop. Formally, Black has a material advantage, but their king is under attack from all the white pieces, and the black rooks can't help him. Black might not immediately lose, but it's unlikely they can defend without significant material losses – they'll have to use their rooks to block the diagonals for the bishops.