What is the ruling on a woman who sends messages and videos about honoring one's parents, or about prayer and other religious matters, to men?

The general rule is that the exchange of admonitory messages and reminder clips between non-mahram (definition) men and women is not religiously prohibited. An example of this is Aisha, may Allah be pleased with her, writing to Mu'awiya, may Allah be pleased with him, to advise him. However, it is preferable for a woman to limit her da'wah to women, as Satan may exploit the door of da'wah (invitation to Islam) and reminders to broaden the relationship between a man and a woman, which could lead to severe consequences.