Conversation with my coachee/coach and remaining questions

Almost two weeks ago, I had the first conversation with my coachee. She was more mature than me in every sense. I was not sure that I could be her coachee, then she encouraged me. After the conversation with her, I wondered whether for a coach, more experience, maturity or knowledge is necessary than for the coachee. Being a coach(maybe 'good coach') was posing a good question rather than giving advice, said the professor. He also emphasized how important it is to listen to the coachee and let her/him find answers through reflections on their experiences and themselves. That's the way dialogue works between a coach and a coachee.
The other question was, as I left a comment on my coach's blog, how could I be so comfortable when I talked with them(my coach and also my coachee). Yes, there may be a bond between us who take this course. I respect them, their maturity and sincerity. So I feel free from their judgment (Judgment is a big keyword to address problems of my life!). Conversations with them were a very pleasant memory, and I'm looking forward to our next conversations. On the other hand, I'm afraid if the conversation does not go well or if I feel a burden about the conversation. (subtle, but constant anxiety even though things go well, I am anxious if it will not be this nice anymore.) Am I going too far away from the subject of 'dialogue'? My dear loved one told me I tried to analyze everything too much. Paralyzed by analysis.