What are the chances that I will have complications during my gallbladder operation?

Likely very low. One's personal risk factors make the greatest risks: smoking obesity prior abdominal surgery jaundice common duct stones pancreatitis but if none of those, very very low.
Very low. Gallbladder removal is one of the most common operations performed in the US and is, thankfully, very safe. Like all abdominal operations, there are risks of bleeding, infection, blood clots, pneumonia, etc. This is somewhat dependent on the health of the patient, but generally less than 1%. A bile leak may occur less than 1% of the time after surgery; this can often be managed non-surgically.