If your planes turn into a truck, you need to move the truck to the gray central point of the airport province.
Gray central point, not the actual airstrip on the map (which is just graphics).
Every unit is connected with a red dot on the map by a white line. The red dot is the true position of the unit/army. You need the red dot that's connected to the truck to move to the gray central point of the province. Then the truck will turn into a plane again.
Your planes can only fly to a destination that's within the circle around the planes (displays when they're selected). You use Patrol, not Move to fly planes somewhere and if you cannot reach the destination with your planes (it's out of range), you need another airport.
To reach a destination find a province centre that's as close to the destination as possible but still within the circle around your planes, then build an airport in that province. You can then fly planes to that new airport using the Move command. Repeat that until you get an airport that's close enough to the destination.