1) I don't think that statement is true. For those who know God and have faith in Him, the proof is in the Bible. Without the Bible, they probably wouldn't accept God's existence. On the other hand, those who reject God would have to believe in Him to reject Him. In what sense have they rejected God when they do not even believe in Him?
Now, if one rejects the existence of God, there is a good chance that their actions are due to a lack of proof that He exists. There is no proof that God exists - the idea of a deity is one that cannot be prove or disproven scientifically. So the second statement is incorrect, since if no proof is enough, there must be proof, though in reality there is no proof.
Proof that God exists or has a hand in the shaping of the Earth and the life on it is mostly a matter of perception. A geologist might dig up a fossil from the Grand Canyon, and proclaim it to be 200 million years old because it is deep in the earth and has features of creatures from that time, while a Creationist might say that the fossil is deep down in the Earth because the Flood put organisms in layers for some reason. For both people, the fossil is proof of their own beliefs, even if the Creationist must overlook evidence to the contrary to state their opinion.
2) I believe it is possible to be in a state where one is unsure of the existence of God, but has not rejected Him. I am an agnostic - I don't know for sure whether or not there is a god because of the lack of proof, but I also don't think there is one for the same reason. I see no reason to reject Jesus or his gift of absolving sins though, I don't think it exists, so why reject it? I suppose some religions or sects might say that by not accepting the gift, I have rejected Jesus, but that is not my belief. I can't accept or reject something if I don't know it exists.
3) No. Like I said above, in my opinion I have not rejected God. I merely ask for evidence that He exists.
4) Yes, the statement may be thought of as saying that knowing God is the ultimate proof and no other proof is necessary. Whoever wrote that statement believes that there is a God, and since he/she knows God, no proof is needed. I know my roommates, so they exist. I don't carry photos of them around with me though to prove this statement. If I happened to have certain types of schizophrenia, I could have made them all up. This question seems to appeal to the idea that proof is relative. What is proof to one person may not be proof to others.
I believe the Pythagorean Theorem is correct. I could work out the hypotenuses of a few right triangles to show this, but I don't think I could write out a mathematical proof of it. This doesn't mean that it is not correct, only that I can't prove it.
5) This statement depends on one's own beliefs. If they accepted a God which does not forgive much, then rejection might be permanent. If they accepted the common idea that Jesus saves whoever asks him to forgive their sins, then rejection would be forgiven and they could go on as a Christian.
There have been many cases of Creationists saying that they used to believe in evolution, but then opened up a Bible and decided the Theory of Evolution is incorrect. It works the other way too, people have doubted the words of Genesis but accepted them, only to be confronted with evidence of evolution, abiogenesis, and the Big Bang which causes them to change their mind. There are also people who have converted from one religion to another, or from a religion to atheism, or from atheism to a religion.
6) Custard has dealt with Question 6 already, I don't really have anything to add to it.
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