Can the Hebrew word "tzipor" mean any kind of flying creature in Genesis 1, or is the word only referring to fowls such as sparrows, hawks, etc.?
Genesis 1 doesn't use 'tzipor', it uses 'ohf' -- "flying thing."
Professor Gerald Schroeder reads this as including insects. My impression is that many centrist Orthodox rabbis, such as Rabbi Hershel Schachter, are okay with Schroeder's reading of Genesis Chapter 1, at least as a possibility.
Leviticus Ch. 11 lists the 'ohf', flying things, that are not kosher, and it includes bats.
I think 'tzipor' may actually be only "bird" birds, but I'd have to track it down with a concordance. But the word isn't in Genesis Ch. 1.