Is it normal to have a lot of gas after a tummy tuck?

Possible. After a tummy tuck the abdominal muscles are tighter. This causes you to feel bloated or full much faster. Your body will get used to this rather quick. Antibiotics and pain medications may also be causing this. Take some yogurt with active lactobacillus for two weeks.
Bloating and gas. It is extremely common to have bloating and gas after a tummy tuck as well as post prandial early satiety (sensations of fullness after small meals). Antibiotics may alter your intestinal contents and narcotic pain relievers may slow intestinal motility resulting in altered bowel habits as well. Probiotic supplements, stool softeners and laxitives may help.
NO. Tummy tucks (witch hazel) are performed outside the abdominal muscle wall and should not impact the intra-abdominal structures. If this is a big problem I suggest you see your surgeon to have his listen to your tummy and check your surgical sites.
No. A tummy tuck without complications has no effect on one's bowel function.