What is the ruling on laughing at a video clip of a veiled woman playing, and is that considered mockery of religion? And is ridiculing a father's concern with regulating internet use mockery of religion? And what is the ruling on mocking those who are concerned with health, and is that considered mockery of religion? And can jokes about returning to school be considered mockery of religion?

There is no sin or mockery upon you in what you mentioned. The cure for obsessive whispers (waswas (definition)) is to completely disregard them, to divert your mind from thinking about them, and to occupy your time with beneficial knowledge, righteous deeds, or permissible recreation. Also, avoid sitting alone, and frequently engage in reading the Qur'an and Hadith (definition) and in remembering Allah. Whoever is afflicted with waswas should seek refuge in Allah and desist from it.