Does a mature girl seeing her parents caress each other in front of her lead to fantasies that may result in something akin to masturbation? And are these fantasies considered a sin that distances her from Allah? What should she do about her parents' behavior, and how can she calm her urges?

Your parents are wrong in these actions that contradict chivalry and modesty, and they have no right to prevent you from wearing the niqab. However, they have a great right over you, so you must honor them and avoid harming them with any word or deed. We advise you to involve some righteous relatives to speak with them. The fantasies that overwhelm you due to your parents' actions, by themselves, do not constitute masturbation, and you are not sinful for them. However, you must strive to repel these thoughts and distance yourself from your parents when they are performing these actions. What helps you overcome lust is frequent fasting, lowering your gaze, closing the doors to temptation, staying away from everything that incites lust, occupying your time with beneficial deeds, and increasing remembrance (dhikr) and supplication (du'a).