Standard young-Earther responses, taken from when I was a young-Earth creationist.

Round Earth: Yes. You sort of have to stretch to interpret the Bible as saying the Earth is round or flat, so it's not exactly a contradiction. Things like "the four corners of the Earth" are obvious metaphor.

Animals on the boat: The "kinds" of animals (Hebrew "baramin") don't correspond exactly to what we call species. There are fewer animals in the ark than 2*(number of modern species); this is considered to be a sufficient answer even though it probably isn't. I don't know exactly what level of generality the baramin are supposed to be; I guess it depends on how much evolution the particular creationist is willing to accept. They'll typically use the example of dogs and wolves being the same "kind," but if that's the level of similarity we're talking about then there'll still be an awful lot of kinds.

Amount of water: The Earth used to be a lot smoother. Shallower oceans, lower mountains, etc. So it could be covered with a more reasonable amount of water. We know this because in the genealogies some guy named his son after the fact that "in his day the Earth was divided." (The word for divided, Peleg, means earthquake or cataclysm or something. This verse also doubles as tectonic plates being moved around.)

I don't agree with these, but thought that to avoid strawmanning I should post the l responses that I would have used. Not that they're much better than the straw version, but this is the kind of thing that would have been said by at least one YEC.