What should a person do who regrets his embezzlement of unlawful money and mixing it with lawful money? What is the ruling on the possessions he bought with this money, such as books and a computer? What is the ruling on his contribution to buying the family home? And is prayer valid in clothes bought with it, knowing that he still possesses a portion of the mixed money?

What you did is theft and a major sin. You must estimate the stolen amount, then return it to its owners, even if indirectly, along with repenting to Allah. If you cannot return it, then donate it on their behalf. You are not obliged to donate anything you bought with this money, and it is not forbidden for you to use it. There is no harm in obtaining a job with that certificate, and the money earned from it is lawful, as long as you obtained the certificate through your effort and study, and not through your theft of this money.