I think that's completely unethical to ask for a deposit. Clients are not supposed to pay in advance for therapy sessions. I would never agree to any of this anyway. This therapist is treating you like a child. You're not a child. Having a 24-hour-cancellation policy is fine, I would never see someone who had requested more than 24-hour notice. I once saw a therapist who requested a 5-day-notice and I was like "lol bye".