Are the taxes and extra fees included in the hotel price my customer sees, or will they be asked to pay more at the hotel?

Yes for the main taxes, and no for a few charges the hotel collects itself. When a room comes back from a hotel booking API, the rate normally includes the taxes the supplier can work out in advance, so the total your customer pays you at the time of booking is the room and those taxes together.

What is usually not included is anything the property charges on the spot. A city or tourist tax, a resort fee, parking, breakfast where it is not part of the rate, and a refundable damage deposit are the common ones. These are paid at the hotel, often in the local currency, and they sit outside the booking you made. Most suppliers send this information along with the room, so it can be shown in your search results, on the booking page and on the voucher your customer carries.

How well that works depends on the supplier. Some send mandatory charges as a clear separate amount that your portal can print on its own line. Others send only a line of text buried in the room description, and a few send nothing useful at all, which means the same hotel can look cheaper from one supplier than another simply because one of them is quieter about the extras.

The sensible thing to do is book a few test rooms in different countries, one in a city that charges a tourist tax and one at a resort, and read what your search results and your voucher actually say. If those charges are not appearing anywhere, it is worth raising, because a customer who is surprised at check in will come back to you and not to the hotel.