Unfortuantely it sounds like you need to use an old fashioned coat hanger to CAREFULLY squeeze through the window edge and use to unlock the door. Take a wooden spoon or something similar to squeeze between the front and rear glass pushing the seal inward and making room for the coat hanger.
You can also use duct tape on the window to grip it and slowly lower it enough to unlock it, this is using several strips of tape and pulling down as straight as possible holding the bunch of tape ends. Search the internet for a better example, but, it works.
The door locks in the R53, R50, and R52 are controlled by the BC1 control module. Unless someone has changed the wiring that would be your #1 suspect.
You can try to change the settings in the BC1 if you have the BMW program NCS Expert or the BMW Coding tool available. Unfortunately, water sometimes drains down into that specific module and causes issues. Other than that, you're left at the mercy of the stealership. Best of luck.
You can adjust the boot to close a bit more on both sides to see if that won't take care of the light issue. As I remember it's on the right side so just adjust that one first a bit to get it to close a bit tighter. You can also unplug the connection at the latch if the light bothers you until you fix it.
the engine control unit has detected a fault light illuminated which in turn reduces ability to gain high revs as a damage limitation exercise , known as limp home , car requires diagnostic computer to check fault codes to indicate faulty component causing ecu to go into limp home mode
your problem is regarding they your new key is not recognized.
If you have changed the ignition, you have changed the key, right?
did you have changed and the chip from the original key into the new one?
There are no self programming procedures for a 2009 Mini Cooper. The best solution is call a few local automotive locksmiths and see if they have the tools to program this. You can save a little money by ordering a Mini Cooper Key Fob Replacement online.
It is likely that you have a wire rubbing on the body somewhere. This will intermittently short on the body and blow the fuse. You are going to need to search the wiring the find where the damage is and repair it. If you keep driving the problem is likely to get progressively worse as the wire gets more damaged.
If you try the window button and hear just a click from the inside of the door - the motor is fine! Problem is in the contacts of the switch that registers if the windows is all the way up. Try this method for quick fix from video below (I know crazy right? But this worked for me).Long term fix - open the door, get the motor connector and use contact cleaning spray on it to restore connection. A lot of mini electrical issues come from corroded connectors