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One classical definition widely accepted among Christians : God is a pure spirit, infinitely perfect, creator and ruler of all things and beeings.
1)There are a lot of explanations, please focus on one or some theologies. One would have to start from the original sin. One explanation is that the world had to be somehow prepared. And God doesn't send prophets the same way he sends the Messiah.
2) In the Book of Exodus, God appears in a cloud or in a fire, so why couldn't he take another form ? One could say that God is everywhere, but more particularly in some places of objects (example : a tabernacle). This is not a consensus among christians. If you believe that God is perfect and infinite, you assume taking an imperfect human form doesn't limit his perfection (see my answer to your third point).
In other words, God doesn't stop beeing God by "sending his incarnation on earth".
The Pharaohs didn't claim to be God, but rather one particular deity among other, which God wouldn't say (For a variety of reasons, it is assumed that God doesn't lie). Before calling them liers, we should focus on what they exactly meant by "gods", because it was very clear that they were dying just like other humans.
The question of idols is another complicated point. What is "worshipping" ? Christians worship God as a spirit (or at least spirit-like) beeing, so even if God was in a stone they wouldn't worship the stone, but God, the same way worshipping Jesus doesn't mean worshipping his little finger.
3) First I want to point out the difficulty of defining perfection. I can't because I'm imperfect. If you consider the bodily needs of Jesus, they are no needs for God. Jesus beeing hungry doesn't make God want to eat something. On the other hand, not beeing able to fully feel hunger or experience death can be considered an imperfection.
There is a variety of more or less complicated answers to your point focusing on Jesus: For example, the human and God in Jesus are separated in essence in Jesus, or Jesus is 50% divine, 50% human. The Roman Catholic and Orthodox Christian point of view is the hypostatic union: Jesus is fully God and fully Human, and (Ratzinger recently wrote about it, I'm trying to express it in English) Jesus is divinely perfect in his following of the will of God (if it wasn't the case there would be no point in a christian religion or worship), and the rest is bit more complicated to analyse.
4) There are occurences of Jesus praying, fasting, and beeing tempted by the devil in the Gospels. The rest of your question is rather sensitive and I can't objectively answer it here because it would be very long. I recommend you read the New Testament and be careful about the Transfiguration, and expressions like "Son of Man" and "Son of God" and their meanings or interpretations. Jesus taught his disciples to pray as himself did, addressing to God as Abba, "Father".