First of all, it's an embarrassing situation. You should try to stay calm. Maybe start by apologizing for the inappropriate behavior in a private moment. Then, it might be a good idea to have an open and honest conversation about privacy and appropriate boundaries in the future.
Even in some more edgy or modern literature, the focus is still on complex human emotions and social phenomena, not this kind of private and inappropriate behavior.
This is a very uncomfortable situation indeed. You should start by taking responsibility for your actions. Let your little sister know that what she saw was not appropriate for her to see. If she has questions, answer them as simply and appropriately as possible. For example, you could say it's a normal but private activity for adults. After that, work on your self - control and privacy habits to avoid similar incidents in the future. It's important to also respect the fact that this might have an impact on your sister's view of you, so be extra careful in your interactions with her going forward.
Getting caught doing such an inappropriate act in school would likely lead to severe disciplinary actions. You could be suspended from school, face expulsion in more serious cases. It also would seriously damage your reputation among peers and teachers.
Well, it's really awkward. Immediately stop what you're doing. Maybe later you can write her a note if you're too shy to talk face - to - face. Apologize for the inappropriate situation she walked into and assure her it won't happen again in such an open way. And try to keep your private activities more private in the future.
It's most likely a rumor. There are a lot of unsubstantiated stories floating around on the internet. Without proper evidence, it's hard to believe such a disturbing story could be true.