Hi, Eileen. You sound like me! I've seen a number of Ts through the years. About 6 months ago I started with a new one and she is completely different from the others. She asks me questions and says things to me that no other T has. Her style and orientation are different, and it's a very good fit for me. She had me find a "safe place" too.
It takes time to trust a new T, but yours sounds like a good fit for you. My T said to "trust my gut" when deciding if I wanted to see her or not. If you feel good about this T, the "weirdness" will lessen and the productive, healing work of therapy will begin.