How bad and for how long will be the effect of general anesthesia on 78 years old patient (my mom)?

There's no way to tell. I'd talk with the doctor ahead of time. Some research indicates that some anesthetics can cause someone to tip over the edge into dementia. Other research doesn't find that true. At any rate, anesthesia can have risks for anyone, and age is a factor. Please talk with the doctor and ask any questions that you may have. My personal feelings are that if the surgery is elective, I wouldn't do it. Your mother should be told of the pros and cons as well.
Good luck,
Carol

I know for my Mom a very mild general took her a bit more than two weeks to recover from. She did nothing but sleep the entire first week. This was something she had to have done and the doctor promised he gave as little as possible. Good luck. Everyone reacts differently so a good chat with the doctor is in order before she makes any decision.