Is it permissible for a preacher to give lessons specifically for women in the mosque, provided that only women gather with him, knowing that he does not seclude himself with any single woman?

There is no legal impediment to holding circles and lessons for women in mosques or elsewhere, whether the lecturer is a man alone or with others, provided that Islamic etiquette is observed, that there is no khalwa (definition) (unlawful seclusion), and that the hijab (definition) shar'i (Islamic head covering) is maintained. It is preferable for the lessons to be held outside the mosque so that women with legitimate excuses can attend. The Prophet, peace and blessings be upon him, dedicated a day to teaching women, encouraged teaching and inviting women and answering their queries, while warning against khalwa with any of them.