If your soft palate is very thick, say about 2 inches from top to bottom, can that cause breathing and gagging issues? how to fix it?

Possibly: If the back of your throat is crowded from a thick soft palate, large tongue, large tonsils or excessive neck fat you can have sleep apnea or other breathing problems. See your doctor for evaluation.

Soft palate: See an Oral Surgeon to evaluate the size (front-to back and side-t-side) of your soft palate, it's thickness top-to-bottom, and it's affect on your airway and swallowing. Once anatomic parameters have been determined the need for treatment can be evaluated.