What is the ruling on taking out an interest-bearing loan to buy a car for commuting to work, and is the income earned considered unlawful?

Your salary is permissible if your work is lawful and performed as required. There is no harm in your use of a car purchased with money acquired through an interest-based loan, as the prohibition pertains to the borrower's liability, not to the money itself. Borrowing with interest is one of the gravest sins and is not permissible except in cases of extreme necessity. You must repent to Allah.