Can the flight booking API tell me if a ticket can be changed to a different date and what that will cost?

Yes, in most cases the flight booking API can tell you whether a date change is allowed and give you an idea of the penalty, but how much detail you get back depends on the airline and on the supplier the fare came from.

When you search, each fare normally comes back with its fare rules attached. Those rules say whether the ticket can be changed, whether it can be refunded, and what the airline charges if your customer wants to fly on a different day. Some suppliers return this in a tidy form that your portal can read and display on its own. Others simply pass back the airline's own rule text, which is long and written in airline language, so you or your staff will need to read it before you quote anything to the customer.

It is worth being honest with your customer about one thing. The airline penalty is only part of what a date change costs. If the new date is dearer than the old one, your customer also pays the difference in the fare, and that can only be worked out at the moment you actually request the change, because seats and fares keep moving. So treat whatever you saw at search time as a guide and confirm the real amount when you process the change.

If flexibility matters to the travellers you serve, check which of your suppliers return fare rules in a readable form, and think about showing a simple changeable or non changeable label on your results page so your agents can see it before they sell.