What is the ruling on mortgaging a house for an interest-bearing loan, then purchasing this house after its forced sale in a public auction? Does this purchase fall under buying usurped property? And what is the ruling on buying this house from the second purchaser to annex it to the mosque?

Borrowing with usury is Islamically forbidden, and the borrower is not obligated to pay the usurious interest, but only the principal of the loan. If the borrower is unable to repay the principal of the loan, the mortgaged property may be sold to settle the debt in two cases: with the borrower's permission or by a court order. The mortgaged property is sold at its fair market value, and the sale of someone under duress is valid if it is rightfully enforced. So, if the mortgaged property is sold to satisfy a debt by court order, its purchase is permissible. It is permissible to buy the house from the second buyer and annex it to the mosque.