Very interesting questions
Here’s my understanding of such things.
Yes it was absolutely necessary for our salvation. Man had separated himself from God through the sin of Adam. This sin had to be atoned for by man, yet through this act man would be saved by the divine.
Christ had to be fully human in order to suffer as a man and fully die on the cross as a man. He had to be fully man to accept the punishment for the guilt of mankind in order to atone for sins of his fellow men (even though he was himself without sin).
Christ had also to be fully divine in order to save mankind, as only God could save mankind, God himself had to be the offended party. It could not be the grace of God to pour out his wrath on an innocent party, so it had to be God himself who suffered and died as Jesus.
Could God have chosen a different means? I guess since we have an om(name removed by moderator)otent God then he could have. However, he has given us the gift of free will and as men we are free to choose what we do. The sin of Adam had to be atoned for and this atonement had to be freely accepted by a man who was without sin (Jesus, as fully human, freely accepted this ). It’s hard to see how else this could have occurred without the incarnation of God as man.
The incarnation and execution of the Son of God was absolutely necessary.