Is it permissible to maintain a Facebook account that includes men and women for the purpose of reporting abusive content, knowing that the account is also used to publish da'wah (Islamic propagation) and scientific content, and private messages are not enabled on it?

A woman adding men on social media can be a cause of fitna (temptation/strife), as Satan exploits their presence together to lead them into private messaging. Therefore, caution must be exercised when adding men. However, if there is a need to add them and you are secure from private messaging, then there is no harm. But if the work requires viewing inappropriate or sexual content, then this is a great door to fitna that is not permissible to enter, and you should avoid it for the safety of your religion.