Four chess problems

More than stating the importance of time, material sacrifices in chess combinations are tangible proofs of the superiority of mind over matter. Your task, dear reader, is to find out the solution of each of the following chess problems. The first two are composed problems and the other two were extracted from (unknown) real games.

Problem 1 - White to play and mate in two.
V. Melnichenko (1958)

Problem 2 - White to play and mate in two.
S. Loyd (1877)

Problem 3 - White to play and mate in three.

Problem 4 - White to play and mate in three.

Solutions: P1: 1.Bh5 / P2: 1.Qa1 / P3: 1.Ng6 hg6 2.Nd5 ed5 3.Qe5# / P4: 1.Qa6 ba6 2.Nb5 Ka8 3.Rg8#