There is no way to confirm your doubts, and even if all your suspicions about his past actions are true, I doubt he'll admit it now. You can try telling your mom, though. As for reducing the current embarrassment, the best you can do is to tell him directly to behave better like change clothes in private, try to be calm, etc. At such an age, people generally do not change so this exercise might be in vain. But, at least you tried.

There's no use wasting your mental energy on this man. Consider the worst case and know that at present, you know better; he can't hurt you anymore. So, ignore him and focus on your studies and career. You have your whole life ahead. Don't let this trauma gnaw away at your mind and health. I know it's hard to ignore such flashes of memories, recurring doubts and creepiness from your own father, but you'll have to think about your future as you are still little. Use whatever privileges you have and work for what you want to be.