Is it permissible for the owners of public da'wah (Islamic proselytizing) pages on Facebook, which include members of both genders, to accept women's comments on their posts, or to participate in group discussions with members?

It is permissible to use Facebook to spread good and to call people to Allah. There is no harm in posting pictures of men, but it is not permissible to post pictures of women if they are revealing their faces, because this incites fitnah. It is permissible for a woman to write phrases of praise or to participate in discussions of beneficial topics.