“Can anesthesia cause liver problems?”

General Anesthesia is not as likely to cause any liver problems now, as in the past, and currently the risk of liver problem occurring strictly due to administration of an anesthetic are very low. Previously, when Halothane was a commonly used inhalation anesthetic, the risk of acquiring liver problems was greater, but even then the risk was a low percentage possibility. Numbers for the risk of Halothane causing hepatitis were generally quoted as around 1 occurrence in about 6000 to 1 in 20,000 uses of Halothane. Even then, most of the cases of hepatitis that occurred following use of Halothane were in people who were older than 40 years of age. When Halothane Hepatitis occurred, it was often lethal. Fortunately, Halothane is rarely used in the United States now, since better (and safer) inhalation anesthetics have been developed.

Yes.

That is very rare. Most medicines used today have little to no risk to the liver, but this question is best addressed to an anesthesiologist.