Yes. Oh my word, so many irksome puzzle rush survival runs where I spend 30 minutes on one puzzle. Gah! Sometimes after 30 minutes I still get it wrong! Sometimes I get it correct after 30 minutes and it is a feeling of relief, but yeah it is tough.
A) Maybe, but generally if you don't see the idea after 10 minutes, then an hour won't help because you are unfamiliar with the pattern or idea at play
B) Depends on the person, but calculation training and study of various pawn structures seems high on that list.
I don't think I have ever done this while studying chess. Have you? I think the most I've done is maybe 10 minutes. And when I mean study or train, I mean that you write down your decision and the variations that you saw without having moved any of the physical or virtual pieces.
A.) Am I short changing my long term chess growth because of my impatience?
B.) What do the best players do in their training? Will they spend gobs of time analyzing a position in their heads before finding out the best move(s)?