No.
To avoid a double-negative (e.g. he "did not not..."
) My answer is that yes, the man, Christ, died on the cross.
Christ's body was flesh and bone, just like yours and mine. His body was put to death.
God cannot be killed.
He was being obedient by accepting the baptism of repentance, although he had no need. Imo, it was an example of humility (God the Son lowering himself to the level of a servant). Speculative personal opinion, though.
He was. It's been speculated that the Holy Spirit descending was visible only to John as a witness to him (John) that Christ was the Messiah - a pov that I personally accept. Others may have a different 'take' on it.