Is what is happening to my sister's husband—his financial setbacks and the illness of his wife and daughter—due to his dealing with usury or his not praying in the mosque? And how can he get rid of these debts and bring blessings into his life?

Your sister's husband deals in usury, which is a grave and cursed evil; its perpetrator, its agent, its scribe, and its two witnesses are all cursed. Congregational prayer is obligatory, and his shortcomings in fulfilling God's rights are a reason for his loss and lack of success. Perhaps these sins are a cause for depriving him of the blessing of provision and afflicting him with tribulation. He must be advised and reminded to repent, and you should pray for his righteousness. As for previous loans, he is only obligated to repay the principal amount without the usurious increase.