Will an abdominal ultrasound rule out/determine all gallbladder dysfunctions?

Not all: Many things are in the upper abdomen: stomach, pancreas, liver, small intestine, gall bladder, large intestine, abdominal muscles, etc... An exam by a primary care doctor can help figure things out. An ultrasound can see the size of objects such as duct sizes, gall bladder size, gall bladder sludge or stones. Sometimes a "HIDA scan" is used to evaluate function of the gall bladder and liver.