Certainly. Christ came to John the Baptist to be baptized.
He was man in addition to God.
No, the baptism of Jesus, or of anyone at that time, was a type, not an actual baptism. It is like the difference between a model car and a car a person can drive.
Jesus told John the Baptist that He should be baptized to fulfill all righteousness. This fulfilled previous prophecy and served as one among many proofs that Jesus was the Messiah.
Jesus did not do this to look more like men, as I gather you are saying.