Possibly the sensor that is installed in the gearbox and that sends the speed signal to the instrument frame has been broken.
In that case, it would not mark speed, nor would the mileage rise, and the doors would not close alone either.
Another thing that may have happened is that the speedometer has been broken in itself (the clock) and in that case everything would work except the needle, even the kilometers would rise. But the open door does not fit me, unless it is a different breakdown that has appeared at the same time.
I do not know if I will have helped you, but the only thing I can tell you is that you check the connection of the box speed sensor and if everything is right, you put the diagnosis to see if something strange is found.
All the best.