What is the ruling on a female student asking her male professor via email about his well-being, or telling him that she is happy with his teaching and that his information and style are excellent? And is this considered "softening the speech"?

Islam has established strong safeguards for interactions between men and women to prevent discord and corruption, and has forbidden every means that leads to them. Corresponding with a male teacher via email using ordinary language is not considered "softening of speech," because what is meant by softening of speech is gentleness and a charming tone in conversation, as is done by women who arouse suspicion. Phrases of flattery and the like should be avoided, as they may lead to an undesirable familiarity and closeness with the doctor. It suffices to limit communication to what is necessary.