Yes, the flight booking API returns a detailed cost breakdown so you can show your customer exactly what makes up the total price. When you search for flights, you will see the base fare, taxes, fees and any surcharges listed separately. This helps your customers understand what they are paying for and builds trust because they can see it is not just one mystery number.
The exact details you get back depend on what the airline includes in their response. Most airlines break down their pricing clearly, but some may combine certain charges together. You can also add your own markup or commission on top of what the API returns, and most travel agency software lets you show that as a separate line item if you want to be transparent with your customers.
When you move from search to booking, the price should stay the same as long as you book within the hold time that the supplier allows. Some fares hold for just a few minutes while others hold for longer, and the API will tell you how long you have to commit. After you book, you will get the final invoice from the airline which may include additional fees if your customer adds things like seat selections or extra baggage, but the core fare and taxes should match what you saw in the search.
Check with your travel agency software provider about how they display the cost breakdown in your portal, and test a search to see exactly what information appears to your customers before they book.