Is it permissible to take out an interest-bearing loan to pay off previous debts if there is no other solution to avoid legal prosecution, and is his current work in delivering food from non-halal restaurants considered unlawful?

Borrowing with usury is forbidden except in cases of dire necessity. Repaying a previous loan does not constitute a necessity that permits borrowing with usury. One must repent from the previous usurious loan. Your work in food delivery is permissible for permissible foods and forbidden for forbidden foods. Whoever fears Allah and relies upon Him, He will provide him with good provision and suffice him in what concerns him.