Maybe all those things are a sign that the T trusts you and sees you as a great client to work with. My T has given me her private number too if I need it. She doesn't watch the clock as much as other Ts I have had.
I've seen 2 other T's before her and neither of them gave me a private number or made me feel special in any way. One of them was very strict about how I could contact her and actually made me feel she didn't like me.