Is money earned from working night security, while sleeping for hours during the shift, unlawful (haram) or lawful (halal), and what should be done to purify the money if it is mixed?

Your salary is lawful (halal), but you are not entitled to the portion of it that corresponds to the time you spent asleep instead of doing the work assigned to you. You must inform your employer of the truth of the matter. If they permit it, then that is fine; otherwise, they have the right to deduct from your salary an amount proportionate to your shortcomings.