Will a hotel booking API tell me by what date my customer can cancel their room without losing money?

Yes, in most cases it will. When a hotel booking API returns a room, it normally carries the cancellation terms for that exact rate along with it, including the date and time after which a charge starts to apply. Your portal can put that in front of your customer before they confirm, so nobody has to guess and you are not left explaining it afterwards.

How much detail you get varies by supplier. Some send a single clear deadline that you can display as a plain sentence. Some send a set of rules where the charge changes as the arrival date gets closer, so you have to show more than one line. A few send little more than a free to cancel or non refundable flag. Rates sold as non refundable will say so up front, and those cannot be cancelled without a loss however early your customer asks.

The thing most often missed is the time zone. A cancellation deadline is normally set in the hotel's local time, so a room that looks safe to cancel in your own evening can already be past its deadline where the hotel is. It helps to show the deadline together with its time zone on screen, and to treat anything close to the arrival date as urgent rather than routine.

Ask your supplier which cancellation fields their API sends and how reliable they are, then make sure your portal repeats that same wording on the confirmation your customer receives.