Faith101: Your questions are very important, deep, and valuable. I’ll do my best to answer them.
First off, you are very correct that Jesus speaks of the Father in the third-person, as if He was just another human being. He ALSO says, however, in Matthew 28:19:
19Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
Notice it says name, singular, and not names? That’s very important, and a valuable insight. So Jesus is the Son, but Son is part of the name of God. We also know that Jesus is the Word of God, as described in the opening of John. Can we think of any things that we can relate all of these things to? If you try, I think you can.
When you think of yourself, in your mind, don’t you view yourself? Can’t you imagine yourself in the third-person, describing your attributes, even having internal conversations? (“Now, Faith101, you know better than that!”) When you think of yourself, or even have internal dialogue, do you become a seperate being? Of course not, and neither does God. The Son is God’s realization of Himself, His eternal understanding of His own Divinity. Being perfectly knowledgable, He has a perfect self-image. This self-image is not seperate, it’s not created because God is eternal and eternally self-knowing. The Son is a description of God knowing God. So, when God comes to Earth, it is the Son, and not the Father, because it is God coming forth from God. When Jesus speaks to the Father, we are witnessing the internal dialogue of God, not two seperate beings communicating.
As for when Jesus says “by your will, not mine”, that refers to the HUMAN will of Jesus, not a seperate being. Jesus’ human will, or you might call it the base nature of humanity that desires to survive at all costs, was submitting to the Divine will that demanded that Jesus die and Rise. In fact, we can say the exact same thing when we do a holy thing that might demand we die, when we become martyrs. Our human nature is submitted to our higher mind; although we get nervous, and our mind screams that we should get out of the trouble, we know that we are doing a holy thing, and we do it. Since God had a human form and body, He felt that aspect of humanity, but perfectly brought it in line with His Divine Will. That is what you are reading with those sayings.
As for Jesus not knowing things that God should know, that’s more a matter of Jesus not being sent to reveal certain things. God deposited everything to be revealed into the physical, human brain of Jesus, so that He could speak it through his physical, human mouth. For example, when you type in a website and hit enter when using a web-browser, it sends you to a website. Now open a typing program and do the same. Does it send you to a website? No, because it doesn’t “know” how to do it. But it’s the SAME computer, and it JUST did it! The computer knows how to send you to a website, but now it isn’t doing it even though you’ve done the exact same thing. That is similar to how it is with Jesus as a man, and the Son as God.