Why for females in singular is मेरी बहनें and plural मेरी बहनें while for males the singular version changes from मेरा भाई to मेरे भाई? Is it always मेरी for feminine nouns?
Yes, the article for males changes from singular to plural, while for females it doesn't. Also a slight correction: मेरी बहन is singular, not मेरी बहनें.
could you use अपनी instead of मेरी here? as in "my own" sisters
Since the subject (वो) and "possessor" (मैं) are different you use मेरी not अपनी