Is it incumbent upon the female supervisor to prevent the posting of pictures of animate beings (such as butterflies or children) in the handicrafts section, and is she responsible for correcting spelling errors in members' responses?

It is not permissible to draw animate beings in their complete form in handicrafts. However, it is allowed if the depiction is ناقص (incomplete) in a way that is evident and makes it impossible for the being to live, such as depicting only the face. Nevertheless, refraining from all of this is better. The sister in charge is obligated to prevent the publication of complete images of animate beings. She is responsible for correcting the mistakes or responses of the members if the section has committed to that. Otherwise, she is only obligated to correct what is fundamentally required by Islamic law, such as verses (of the Quran).