TSH should not be so high. Your mother probably needs some T3 as well as T4. 200 of T4 is high dose.
Her other numbers are ok, actually quite good with low bilirubin, normal platelets and undetected HCV.
Has Hepatitis B been checked?
Low thyroid is key problem to fix, please get doctor to give small dose of T3 and check TSH in a week.
Live donor is safe enough if surgeon is good.