Also, amusingly enough, it features a spherical Earth. And I have to wonder how they'll fit "one couple of every species of the Earth" in that ship, huge though it is, without involving Gallifreyan technology.

I'd strongly caution against fighting a false version of your opponent. Even among biblical literalists, very nearly none believe in a -spherical- (EDIT: flat, thank you for catching the typo) Earth (often citing parts of the bible that call the world a sphere!), and that's been the case for over a millennium. And while the movie probably will have impossible space CGI shenanigans, even the Creationist idiots tend to think of things in terms of "kind" rather than "species" (and often don't understand the later's definition), and try to create some artificial dividing line between macroevolution and animal husbandry.

And about all the water on Earth not being sufficient to actually flood everything; will they have God miraculously, spontaneously and temporarily generate water for that specific purpose, and then later remove it?

The original Jewish version would probably go that way, since it was closer to a cataclysm/Ragnarok event in that belief structure. Modern Christian translations generally just turn it into rain. Given that the actions of a literal magic sky being are part of the premise...

That's not to say Biblical Literalism or Creationism is particularly coherent, nor that it's likely to be a good movie, of course.