Yeah, this is another conversation that is impossible to bring to a logical end. True Science can't speak on the past because the past isn't observable, and observation is a requirement of true science. (Didn't hear that when you did the origins segment of your Biology class in College, did you?!?!)
However here are some thoughts...
"1)If a just, fair God exists, why do tiny children die of wicked diseases?"
We live in a fallen/corrupt world and are born into sin physically and spiritually. In the very same context, is physical death, then, necessarily the ultimate evil, or is it just a transition?
"2)If God has been here all along, why were and are millions of people around this world ignorant of his existence and your "one true path?" "
As to the existance of God, they're not. Natural revelation, as kirby described in "infinate order" points man to God. Man's need for God and spiritual hunger for Him leads to the rest.
"3)How do you explain Neanderthals?"
Neanderthal has been proven to be a skeleton of Modern Man suffering from Ostio-Arthritis. Another point where Darwinists conceal further discovery. Neanderthal and several others in that line of images from ape to man have been thouroughly debunked and should be eliminated, but of course they're not. That would upset a world view.
Did you know that when "Lucy" (australopithicus) was discovered, just prior to that, the "scientist" who found the bones was flying over the landscape and was quoted as saying, "...anything we find down there is going to be at least 200 million years old!" Very scientific!
Speaking of that, same kind of misinformation, or concealed discovery, with Carbon 14 dating. It's regularly touted as "accurate" and "scientific" but did you know that to test with the carbon 14 method, you have to enter an estimated age into the computer? They tested a LIVE clam (3-7 year life cycle) and it turned out to be over 200,000 years old according to carbon 14.
"4)Are there Christian symbols in cave drawings?"
There are Biblical symbols, the worldwide flood, Deity, et.al. Cavedwellers lived about the time of the great hunter Nimrod, and the Tower of Babel, that was before Christ. "...Faith accounted to him as Righteousness..." the era of God's Grace based on Faith, just like AD, but now we have more of the picture, and more assurance of eternity with God.
"5)Why did your wonderful God allow the Crusades?"
Why does he allow people to slander Him? To publicly declare His nonexistance? Same answer: He gave us a free will, and won't step in and force any human to do or not do anything. Misguided or otherwise.