About unusual forced mates Are there 'legitimate' chess positions were say white can force a mate by sacrificing  4 of its pieces in succession one after the other? Can this be done even if white has less material than black?
There are many beautiful sacrificial games out there and if you look at composed position you will find even more sacrificial combinations leading to mate. This is one of the most famous games, Anderssen-Kieseritsky from 1851, called "The immortal game":

rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1
1.e4 e5 2.f4 exf4 3.Bc4 Qh4+ 4.Kf1 b5 5.Bxb5 Nf6 6.Nf3 Qh6
7.d3 Nh5 8.Nh4 Qg5 9.Nf5 c6 10.g4 Nf6 11.Rg1 cxb5 12.h4 Qg6
13.h5 Qg5 14.Qf3 Ng8 15.Bxf4 Qf6 16.Nc3 Bc5 17.Nd5 Qxb2 18.Bd6
Bxg1 {It is from this move that Black's defeat stems. Wilhelm
Steinitz suggested in 1879 that a better move would be
18... Qxa1+; likely moves to follow are 19. Ke2 Qb2 20. Kd2
Bxg1.} 19. e5 Qxa1+ 20. Ke2 Na6 21.Nxg7+ Kd8 22.Qf6+ Nxf6
23.Be7# 1-0


There surely are games out there that concur even more exactly to your specifications, but generally sacrificing pieces to mate the enemy king is a normal occurrence in chess games.