Will my customers see how much baggage is included in the flight price before they pay?

Yes, in most cases the baggage allowance is shown before your customer pays, but how much detail appears depends entirely on what the airline sends back through the API for that particular fare.

Full service airlines usually return a clear cabin and checked allowance for each passenger, either as a number of pieces or as a weight, and that information is displayed on the search results and again on the review page before payment. Budget airlines and some deeply discounted fares are less generous with their data. Sometimes the allowance depends on the fare family the customer picks, and sometimes the airline sends nothing at all. When that happens, the system can only display what it was given, so your customer may see a note saying hand baggage only, or that the allowance must be confirmed with the airline, rather than a firm figure.

Paid extra bags work the same way. Where the airline supports selling baggage through the API, your customer can add an extra bag during booking and it is included in what they pay you. Where the airline does not, the only way to add a bag is on the airline's own site or at the airport, and you should tell your customer that at the time of booking. Allowances for infants and children often differ from adults and are not always returned separately, so treat those with extra care.

The best thing to do is run test searches on the routes you sell most often and compare what your site shows against the airline's own page, then add a short line in your booking terms asking customers to confirm baggage directly with the airline before they travel.