When I insert and turn the key, nothing happens. I just freely turns and not engaging the lock. Central locking by remote works fine and unlocks the car, but it would be nice to have a key option as a backup. Can it be fixed or do parts need replacing?

That sounds like the lock barrel has failed..

This will turn even if the sliders are not in the correct position, like if I use a screwdriver? I've used CRC 5-56, not helping. Remove it and try to losen the sliders? Any guide for removing the cylinder?

Theres a thread on replacing the door lock microswitch, which includes removing the lock cylinder.

When i say its failed as per your description it sounds like the actual lock bar has failed i.e. the thing the cylinder moves to operate the lock. If it was just worn away in the barrel id imagine a teaspoon would turn the barrel and operate the lock. Yours is just turning the barrel. So its a "deeper" mechanism issue.