What should a wife do if her husband dies and she has debts whose creditors and amounts she does not know, and is it permissible to pay in installments what she knows of the debts?

The deceased's debt must be paid immediately if he left enough to cover it, because "the soul of a believer is suspended by his debt until it is paid off." Debts for which you know the creditors should be paid immediately and not in installments unless with their permission. As for deferred debts, the majority of jurists (Shafi'is, Hanafis, Malikis) held that they become due upon the death of the debtor, while Hanbalis believe they do not.

Regarding debts whose creditors are unknown, if you are certain of them, you must keep them as a trust until their owner is known. If you despair of finding the owner, then give charity on their behalf. Some jurists mention handing them over to a just ruler, but this is not available in most countries. All of this applies if there is an estate; otherwise, there is no obligation to pay it off on his behalf, and whoever volunteers to do so is a doer of good.