There are many theories about why Jesus had to be born of a virgin, but I think the simplest one is that Jesus' birth had to be miraculous as one of the signs to prove his being the Messiah. As for the next question, why he was not under the curse of all humanity, that's a whole different can of worms (which, as you may know, is my specialty :0 ). But let me come back to that in a minute.
God, being a Trinity, can be in more than one place at a time. The Father always was, is, and will be on his throne, so heaven was never without its king. Jesus never lost his divinity even while human; he was both fully God and fully Man at the same time. As is the case for everyone who ever walks the earth, Jesus' physical body was "made immortal" after he rose from the dead, but it evidently resembled his mortal body because he said to Thomas, "see my hands and my side". Paul writes in 1 Cor. 15,
"15:42 It is the same with the resurrection of the dead. What is sown is perishable, what is raised is imperishable. 15:43 It is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; 15:44 it is sown a natural body, it is raised a spiritual body. If there is a natural body, there is also a spiritual body. 15:45 So also it is written, “The first man, Adam, became a living person”; the last Adam became a life-giving spirit. 15:46 However, the spiritual did not come first, but the natural, and then the spiritual. 15:47 The first man is from the earth, made of dust; the second man is from heaven. 15:48 Like the one made of dust, so too are those made of dust, and like the one from heaven, so too those who are heavenly. 15:49 And just as we have borne the image of the man of dust, let us also bear the image of the man of heaven."
The trinitarian nature of God is not the easiest thing to grasp, but God expects us to understand what he told us in the Bible. What I see there tells me that even though Jesus spoke often of his own spirit, the Holy Spirit is a separate entity. After all, when Jesus was baptized the Holy Spirit "descended on him like a dove". This would not be possible if the spirit of Jesus were identical to the Holy Spirit. Otherwise we'd have to believe that Jesus had no spirit at all until his baptism! (BTW, that incident is an excellent argument for the Trinity, since all 3 "entities" of God were there at the same time.)
Now back to the "sin nature". (takes a deep breath and prepares to run)
I've got documents that detail this on my web (link below), so I'll just try to summarize here. Keep in mind, though, that you really need to do careful reading of the scriptures and not just my summary.
Genesis tells us that everything God made was originally "very good", and believe it or not, that includes mankind. Some believe that God must have created Adam and Eve with a sin nature, but that would definitely not be a good thing. Given that they were not created as sinners, what made them sin?
The answer is free moral agency. God did not create robots but people "in His own image", the image of a free moral agent. Now "enter the dragon": the serpent comes along to tempt, and man falls like a house of cards. Sin thus entered the world, and death through sin. What kind of death? The context clearly indicates physical. This curse was placed upon the entire earth, not just man, so it could not mean spiritual death, since the soil and animals, and yes, human babies, could not commit sins against God.
If "nature" did not cause Adam and Eve to sin, then why is "nature" blamed for our sin? We are their descendants, the children of those made in God's image. If Adam and Eve had "dead" spirits then they could not reproduce anything spiritual. In other words, if spiritual death can be inherited, then so can spiritual life. The children of the saved would all be born saved if spiritual attributes could be passed down through inheritance. Why do we sin, every one of us who ever lived? Because we are free moral agents who are surrounded by temptation.
So to answer your question about whether Jesus was under the curse of all humanity, the answer is no. Had he not laid down his physical life, he would have lived forever because, unlike the earth and animals, he was/is a living soul. That Jesus committed no sin is truly an amazing feat, yet another reason to look up to Him, who "was in all ways tempted as we are, yet was without sin". Notice the parallel between temptation and sin? It's temptation that caused Adam and Eve to make a poor choice, and it's temptation that causes us to do the same. That is why Satan can rightly be blamed for his part in goading Adam and Eve to sin, but why Adam and Eve were also held responsible for their own part. That is also why I believe babies who die go to heaven.