I'm sorry to hear about your situation with your step mother. I'm not sure how your relationship is with your father, but would it be possible to chat with him about what you overheard or how you're feeling? If you can, that may be the best way to start. So far as the confrontation goes, I completely understand wanting to avoid it. I am not good with confrontation, especially where I can see negative consequences which have the potential to affect others besides myself.
That being said, keep in mind that your step mother's issue with you is her issue, not yours. One of my sister's favorite sayings is, "if someone gets your goat, it's your goat". I can definitely empathize with how hard it is to have someone be sugar sweet to you when you know that they're completely different behind your back... it sucks for sure. But it sounds to me like your step mother is very insecure in her relationship with your father. She sounds to me like she's afraid of being replaced. So any amount of time or affection that he places onto another female (even his own daughter) will trigger her to feel jealous and out of control of the situation. It sounds to me that you know that it's ridiculous for her to think that your father would view you in any other way than what is normal for a relationship between a father and daughter. You can rationalize for yourself that her accusation is ridiculous and completely out of bounds.
Is it possible for you to accept that there is not the possibility for a positive relationship between you and your stepmother? Like, would you be able to accept that, although she's nice to your face, that she is not actually your advocate? If so, if you can let that go, you may be able to continue to spend time with them as if there is no issue. Whereas, confronting your stepmother face to face may cause her "falseness" to disappear, and be replaced by up front animosity.
And so far as her fishing for information, I'm making an assumption here, but it sounds to me like she wants to know as much about you as she can so that she feels like she has control over you. I think it's fair for you to withhold information from her that you are not comfortable with sharing.