What is the Islamic ruling on my colleague buying a car with a loan she takes from the bank, and then I agree with her to pay her back the amount in monthly installments?

It is not permissible to agree to buy a car with a usurious loan, because it is an agreement to disobey Allah and to assist in what is forbidden, and a transaction involving unlawful money. Allah has forbidden disobedience, causing it, and assisting in it. The Prophet, peace and blessings be upon him, cursed the one who consumes usury, the one who feeds it, its scribe, and its two witnesses. You should rather advise your colleague and deter her from borrowing with usury.