Sure valid points. I don't think the bible is trying to be scientific though. That said, the dimensions of the ark are mathematically feasible. The fact that Noah was several hundred years old when he built the thing is not.
Science has looked at whether a flood event happened and they believe there was an event. Obviously not the whole world, but as far as the people who lived in that region, it was the whole world as they understood it at the time. (certainly their corner of the world).
I do not follow the bible or any doctrine, but I do not believe the bible is fake. It is a very loose account of history and the thoughts of people who lived at the time. Then translated over and over and as the church evolved, I'm sure plenty of chapters or stories were omitted if it didn't fit the church politics of the times.
As a people, these things make up a part of who were are and where we came from culturally. That is why, regardless of what I think, they should be preserved