If anyone has any idea about people surviving this advanced stage of cancer...then do reply. If you can suggest any beam radiation therapies...and also if you know about any specialists dealing with such advanced stages,do inform me..

-Assuming histology has been obtained and confirms the radiology report: I dont know of any such stage IV cases being cured, the prognosis sounds correct. Stenting of the neck of the gallbladder to relieve the symptoms caused by the buildup of bile in the liver may be beneficial, brachytherapy of these stents can help to extend their use (timewise). Otherwise make sure your mom is kept comfortable with sufficiently strong painkillers if and when she has pain.

-(judicious) External beam radiation therapy is sometimes possible to alleviate pain from mets. So you have to help your mother assess what they are recommending as treatment, assess her current symptoms and what is the best way to palliate the symptoms, whether chemo, RT or hospice (care by an experienced RN or doctor to make sure that she does not suffer and has good quality of life, for whatever time remains for your mother).