Can the hotel booking API show whether local taxes and extra hotel fees are included in the price?

Yes, in most cases the hotel booking API can tell you what is included in the price and what is charged on top, because the rate it returns is usually broken down into the room rate, the taxes and any extra fees.

How this appears depends on the supplier behind the rate. Some suppliers send a single total that already covers taxes and service charges, while others send the room rate and then list the taxes separately so you can display both. Charges that a hotel collects on arrival, such as a city tax or a resort fee, are normally flagged as payable at the property rather than added to the amount your customer pays you, so you can show them as something the guest should expect at check in.

It is worth being honest about the limits. The API can only pass on what the supplier declares, and not every hotel reports every local charge, so now and then a charge appears only in the hotel's own terms. Where that happens, the rate conditions text that comes back with the room is the safest place to look, and it is sensible to show that text to your customer before they confirm.

Next, run a few test searches for the cities you sell most and compare the price breakdown you receive with the hotel's published terms, then make sure your booking page shows any amount payable at the property clearly, so your customer is not surprised at check in.