Is it permissible to combine the intentions of charity (sadaqah), zakat, and expiation (kaffarah) when donating money, while leaving the determination of the type of intention to Allah Almighty?

The intention must be specified when disbursing money. If there is no intention, the money is considered an absolute charity and does not count as zakat (definition) or expiation. Intention is a condition for giving zakat, and likewise for the fidyah (definition) (ransom) for fasting, as it is a financial act of worship like zakat and expiation. As for the doubt of money being mixed with unlawful gains, if it is merely a suspicion, it holds no weight; but if it is a confirmed fact, it has other rulings.