Rewan Demontay already has a great answer. However, I would also like to add this 'self-solving' chess problem from Tim Krabbé. Here, all moves are forced and will lead to a checkmate.
[Title "Tim Krabbe - Self-solving chess problem"]
[FEN "K1k5/P1Pp4/1p1P4/8/p7/P2P4/8/8 w - - 0 1"]
[startflipped ""]
1. d4 b5 2. d5 b4 3. axb4 a3 4. b5 a2 5. b6 a1=any 6. b7#
Although it does not completely satisfy your type 3 requirement that checkmate is not guaranteed in the first ply, I think it is a nice little puzzle that has some similarities with your question.