This is actually several similar questions compounded together. I hope this doesn't come off the wrong way, but it seems like Noah had the opportunity (and I'm sure he had the motive) to leave the ark before he actually did, and I'm wondering if someone can explain why.
Starting in Bereishit Chapter 8, Verse 4, it says Noah's ark came to rest on the mountains in the seventh month. So why not leave the ark then? (I believe Seder Olam ch. 4 says because the bottom of the boat was 11 cubits below the surface... but drying at a rate of 4 cubits per month seems a bit slow compared to how fast it must have dried afterwards.) Then it says in the tenth month that the mountain peak was visible. So why not leave the ark then? 54 days later the dove couldn't find anywhere to land... What was wrong with the mountain peak, I mean it had two months to dry in the sun by then? Another week later, the twelfth month, the dove found an olive branch and Noah knew the waters had gone. Aside from the question of how did a new olive tree grow so fast, why didn't Noah go and get some leg room and let the animals walk around outside for the first time in a year right away, when it was good enough for the dove? Then, why does it say the waters had dried up in the first month if the dove was successful in its mission to find land the previous month? Why not go out now? And then a month later, the second month, it says the ground dries again, why did it even mention when it dried the first time? And then if God told Noah when to leave the ark, why did he bother send out birds and looking to see if the ground was dry?