It's hard to determine whether she has a hepatobiliary/gallbladder problem, given the numbers you've posted. Her overall liver numbers show that her liver is healthy. Her synthesis function is good and producing a normal levels of Albumin. Her excretory function is surprising good considering that she apparently has a stone lodged in her CBD. The total Bilirubin is within normal limits - do you also have the breakdown of direct Bilirubin as well? Also her Alp (alkaline phosphatase) levels would be very helpful as well. But her Alt and Ast liver enzyme levels are very good and low, indicating that her liver isn't currently under any stress. This is consistent with her normal Bilirubin levels. A larger stone would usually cause impeded bile flow, backing up into the liver and causing damage which would raise the Alt,Ast levels. The stone does seem to be locally expanding the CBD, since you indicate that a dilated duct is noted along with Cholecystitis.
Since the CBD is distally dilated, have they been able to do some additional MRI imaging yet to augment the CT data? Combined MRI/MRCP sequences would hopefully provide some very needed information on any surrounding pathologies. The noted cyst and hemangioma are benign entities and not typically dangerous.
It's great that you have this baseline set of data on her liver's current status. The treatments involving antibiotics will tend to cause minor liver damage (antibiotic can be hepatotoxic) and the normal enzyme levels will likely begin to increase. But this is normal and her doctors will likely be monitoring things as the treatment progresses. The vomiting of yellowish liquid is likely not related to the CBD stone since her Bilirubin levels are normal and a backup of bile isn't indicated.
The elevated Sed rate shows her body is doing battle. Have the doctors indicated to you whether they think that it's due to her hepatobiliary/gallbladder problems? Also, have they been able to sample her ascites fluid yet to make a determination of it's source? They can spin the fluid down and sift the cells to do cytological analysis to help narrow down the differential diagnosis.
Hope we can help further when new data is gathered. Please let us know if you have any question. Take care and wishing for good answers for your mother.