Is it permissible to combine and shorten the 'Asr prayer with the Dhuhr prayer in the city before traveling by plane, knowing that the plane's departure time is before the entry of 'Asr time? What is the ruling on that, and what is the correct action in this situation?

It is permissible for a resident to combine two prayers when there is a difficulty in performing the second prayer at its appointed time. Combining prayers is broader than shortening them. You may advance the Asr prayer with the Dhuhr prayer in your city if you predominantly believe you will not be able to perform it at its appointed time due to travel. If the airport is outside your village, you may shorten the prayer, but if you are a resident of it, you do not shorten. The reason for shortening prayers is travel, while the reason for combining them is necessity and an excuse to alleviate hardship from the Ummah.