Is it permissible to shorten the Dhuhr prayer and combine it with Asr at the airport after the time for Dhuhr has begun in the city and an hour before traveling?

It is better to perform the Dhuhr prayer at the beginning of its time if there is no intense heat, even though performing it in the middle or at the end of its time is permissible. As for shortening and combining prayers at the airport: If the airport is outside the city you departed from, then what you did by shortening and combining prayers is correct, because you had begun your journey. However, if the airport is within the city, it is not prescribed to shorten prayers until after passing the city's built-up area. In this case, you must make up the prayers that were performed shortened.