One at a time. Regarding the Bible on bats and birds.
The Hebrew word ohph, at Leviticus 11:13, in older translations, may read fowl, because at one time the English word fowl applied to all winged flying creatures, not exclusively to birds as it does now.
The Hebrew word for bat is ‛ata·leph.
The Hebrew word for flying creature or fowl (as in all flying creatures including birds, bats, and insects) is ‛ohph.
The Hebrew word for birds in general is tsip·pohr′.
The Hebrew word for birds of prey specifically is ‛a′yit.
The Hebrew word she′rets is drawn from a root word that means to "swarm" "or teem." In noun form applies to small creatures to be found in large numbers. (Exodus 8:3 / Psalm 105:30) In scripture it first applies to the initial appearance on the fifth creative day when the waters began to swarm with living souls. Genesis 1:20
The law regarding clean and unclean things demonstrates that the term applies to aquatic creatures (Leviticus 11:10) winged creatures, including bats and insects (Leviticus 11:19-31 / Deuteronomy 14:19) land creatures such as rodents, lizards, chameleons (Leviticus 11:29-31) creatures traveling on their "belly" and multilegged creatures (Leviticus 11:41-44).
It isn't about taxonomy it is about language and translation.