Why does the questioner feel shy about speaking the truth to people and correcting their mistakes, and about enjoining men to lower their gaze, or speaking with Muslims when they do something incorrect, despite their conviction that no one should be feared or pleased except Allah?

A woman is not obligated to directly invite non-mahram men to Islam due to the potential for fitnah (temptation/discord). She should, instead, cultivate herself in obedience to Allah and fulfill the rights of her husband, family, and children. She should engage in da'wah (inviting to Islam) within women's communities to the best of her ability. Shyness does not justify abandoning da'wah, as it requires perseverance and patience, for Allah Almighty says: (By the Aṣr [time]. Indeed, mankind is in loss, Except for those who have believed and done righteous deeds and advised each other to truth and advised each other to patience.) As for da'wah via the internet, it is desirable but contains pitfalls from which few are saved except those whom Allah protects, and it requires profound knowledge and sincere faith. The hijab is obligatory for a Muslim woman to protect her from the harm of evildoers, and she must distance herself from bad company.