Why did Moses say to the righteous servant: "If I ask you about anything after this, do not keep me company," and how could he say that when he was accompanying him?

There is no difficulty in the verse, for Al-Khidr and Musa (peace be upon them) became companions after Al-Khidr agreed to accompany Musa, which is why Musa said what he said. Musa was fair to Al-Khidr when he excused him the third time. It is probable that the meaning of "then do not accompany me" is "do not consider me your companion," or "do not let me accompany you."