Is it normal for my baby to be choking, sneezing, gagging, and coughing regularly?

No. Normal babies occasionally sneeze and cough, uncommonly gag and rarely choke. If your baby is regularly doing any or all of these, you should arrange for an appointment with your pediatrician as soon as possible.
No. Discuss it with your doctor make sure that your baby does mot have a breathing ot swallowing problem.