Admittedly it's been years since I read Genesis, but it doesn't go into the specifics of how various animals were created like the rib bit with Eve, does it?
No, it doesn't. It doesn't put itself forth as a science book. It's telling the who and the why, not the how.
Now, I personally believe in a created Adam, and a created Eve. That doesn't mean I believe they were the only or first creatures we today would recognize as humans from fossil remains. There are two creation accounts in Genesis, one right after another. Also, there are other parts that talk about the sons of God and the daughters of men. The common parsing of that is that the sons of God were angels. I don't necessarily think that has to be the case, and often wonder if the people from created ancestors were intermingling with people who had evolved from creatures originally created as apes.
I like the part of Inherit the Wind where the Darrow character says during his crossexamination of the opposing lawyer something to the point that, since the Bible says that God didn't create the Sun and the Moon until later in the six days, that the length of "a day" before that could have been longer than the standard 24-hour one, and gets the other lawyer to admit to that possibility.
That's very much how I look at it. Per Genesis, light was first created (by God, but its source was not the sun), but the sun, moon, and stars weren't set in place until day four. Genesis is telling us that the being present at the creation it recounts was an eternal (hence timeless) being. Now, without the celestial bodies by which we finite creatures mark time, when someone who thinks he's a literalist tells me I'm supposed to believe Genesis' days 1-3 were 24 hour days, I tell them I can't, because I take the biblical account seriously, and it doesn't tell me that, and actually seems to indicate otherwise, since that by which we mark the hours wasn't yet created.