I think you need to get the transmission replaced with a used unit. Call salvage yards in your area. Often they can find a used transmission and install it for you. As for the rest of the repairs they sound like a lot dealer service dept. “padding” to up their profits. After you get the transmission issue resolved then find an independent shop to see if they agree with the Mini dealer service dept. on what the car needs.
You really need to decide if you want to keep this car? My opinion is get the transmission fixed, sell it and don’t get another Mini.