Question: "Gods sense of time if he thinks a day is 24 hours"
General Answer: God exists outside of time. Time is just something that man made to better understand creation. Because God is omnipresent, he has always existed which is something that us as sinful humans will never be able to comprehend.
Specific Answer: We live in a physical world with its four known space-time dimensions of length, width, height (or depth) and time. However, God dwells in a different dimension—the spirit realm—beyond the perception of our physical senses. It’s not that God isn’t real; it’s a matter of His not being limited by the physical laws and dimensions that govern our world (Isaiah 57:15). Knowing that “God is spirit” (John 4:24), what is His relationship to time?
In Psalm 90:4, Moses used a simple yet profound analogy in describing the timelessness of God: “For a thousand years in Your sight are like a day that has just gone by, or like a watch in the night.” The eternity of God is contrasted with the temporality of man. Our lives are but short and frail, but God does not weaken or fail with the passage of time.
In a sense, the marking of time is irrelevant to God because He transcends it. Peter, in 2 Peter 3:8, cautioned his readers not to let this one critical fact escape their notice—that God’s perspective on time is far different from mankind’s ( Psalm 102:12, 24-27). The Lord does not count time as we do. He is above and outside of the sphere of time. God sees all of eternity’s past and eternity’s future. The time that passes on earth is of no consequence from God’s timeless perspective. A second is no different from an eon; a billion years pass like seconds to the eternal God.
Question: "Adam and Eve were Neanderthals or looked just like us" "if the Big Bang happened or if god just snapped his fingers and they appeared"
General Answer: Neanderthals are a construct of humans as well just looking to answer questions without including God. Adam and Eve were created in God’s image like us.
Specific Answer: Neanderthals were human. They used fire, buried their dead with rituals, wore jewelry, possibly wore make-up, and even organized and heated the water in their homes. They were humans, made in God’s image and descended from Adam and Eve just like us. Neanderthals simply represent a people group that formed after the dispersion at the Tower of Babel, after the Flood, just a few thousand (not hundreds of thousands) years ago. They had unique characteristics that likely became more prominent as they were isolated from other people by the divinely created language barrier. So it’s to be expected in a biblical worldview that modern humans and Neanderthals share DNA.
link: Where Does Neanderthal Fit in the Bible ? http://www.genesisandgenetics.org/2013/11/08/177/
link: Who was Neanderthal man? http://www.biblestudy.org/basicart/who-was-neanderthal-man-was-he-the-missing-link.html