Is it permissible to purchase a store from someone whose wealth and business are based on unlawful means, knowing that the price of the store will be paid to him in monthly installments without usury?

What you asked about has two cases:

The first: That the goods are inherently unlawful, like alcohol. In this case, it is not permissible to buy them.

The second: That the goods are permissible. This has two sub-cases:

The first: That all the store's money comes from unlawful sources. In this case, it is not permissible to buy from it.

The second: That its money is mixed with both lawful and unlawful sources. In this case, there is no harm in buying from it because the Prophet, peace and blessings be upon him, dealt with the Jews, even though their wealth was often not free from unlawful elements.