Most of Twice have co-written at least some songs (the only one I'm not sure about is Tzuyu). I think Chaeyoung is the most prolific so far (I suspect that little dark horse is gonna be the first to fully write her own song).
Dami has co-written a few of Dreamcatcher's songs.
And Soyeon does produce as well as write; I think most of I Made was at least co-produced by her.
Sadly there aren't many self-producing girl groups, but I know LE from EXID produces all of their songs. Solar and Moonbyul have also produced/written some Mamamoo songs
For female soloists, Sunmi and Heize also produce their own songs
I’m not sure the difference between producing and writing, but I know that the mamamoo manners are involved in a lot of their projects and solo projects
Gidle, EXID are the only ones that I believe full self-produce. But there are other groups that will contribute a lot of lyrics and composing. Le Sserafim and izone are ones that come to mind.