Are all the conditions of semen required for it to be ruled as such? And is the thin white fluid discharged after watching permissible family films—without feeling desire—considered semen that necessitates ghusl and invalidates the fast?

The ideal solution to your problem is to disregard these whisperings (waswas). If you doubt the validity of your prayer or fasting, the default is that they are valid, and they are not invalidated by mere doubt. If you doubt whether what came out is mani (seminal fluid) or madhi (pre-seminal fluid), you have the choice to consider it either. Fasting is not invalidated by the emission of madhi or mani without masturbation. These whisperings are a ploy by Satan to make worship burdensome for you.