Hello Zoo,
K0 carb slide is not exactly as K3. But from my K3 experience - the cutout section at bottom skirt of throttle valve faces to the airbox. But the keyway slot in the valve is designed to slide in the male key on the carb body - so you should only be able to put it back in the right way...from memory.
Can't answer re the needle removal as mine has screws and base plate holding in the needle. Hopefully there is a higher class of guru online to help you further Zoo.
Regards
Mark