Oh wow.. Nice question. When i started to break the sentence, only then did I find the actual mistake.
Striking out the modifiers (prep. phrases), we have
Studies have found that deaf children
from American families who identify themselves as culturally deaf, and use sign language, are generally on a par with hearing children
in terms of reading and writing, because they have been exposed to language
since birth.
Simply, the statement says, 'deaf children are generally on par with hearing children, because ....
The construction is of type "subject + linking verb + object ..." which is correct.
A and use sign language, are generally
Sounds good. B using sign language, are generally
the verb+ing followed by comma modifies the entire phrase preceding it; which is wrong. Also, not parallel. C use sign language, and are generally
and should introduce an independent clause or introduce the end element of a list. Both are not happening here. D and
using sign language are generally
identify and using are not parallel. E and use sign language, generally
linking verb / main verb missing.