No. Your baby's cold will not get worse because of being on an airplane, though sometimes the dry air can make them seem more congested temporarily. During first few days of the cold, symptoms may still be worsening, but it isn't due to the air travel. It is fine to travel as long as your baby isn't running a high fever, having trouble breathing, or acting very uncomfortable, and is feeding well.
No. The infection will not worsen, but your baby may be bothered more by the symptoms. A stuffy nose makes it difficult for your baby to equilibrate pressure in his/her ears. If possible reschedule the trip to avoid discomfort to your baby and to avoid spreading the cold to other passengers on the airplane.
No. Airplane travel won't make the symptoms of a cold worse, or make them last longer. The pressure changes may drive fluid into the middle ear though, which potentially could lead to an ear infection-- but still, if your baby isn't feeling too miserable, it's fine to go on a plane.