Is it correct to say that Allah knew from eternity the choice of the disbeliever for disbelief and the believer for faith, and He wrote that for them in the Preserved Tablet based on their choice?

Belief in divine decree (Al-Qadar) has four levels: knowledge, writing, will, and creation/formation. Their chronological order is that knowledge is eternal, then writing, then will and creation, which are simultaneous with the occurrence of what is decreed. This does not negate the servant's will and acquisition of their deeds, for affirming Allah's will does not negate the servant's will.