How long does general anesthesia affect body?

It depends. There should be no long lasting effects from general anesthesis itself. The risks of anesthesia depends on your underlying medical conditions. Ga is taxing and stressful to the system, especially if it is a complicated and lengthy surgery. The surgery has more possibilities for post-op complications but you still have to be aware of breathing issues, infections, bleeding, BP stability, etc.
Usually 24 hours. The effects may last up to three days. Normal kidney and liver function help to clear the medications used in anesthesia.
3 days. Modern anesthetics are essentially removed from the body completely within 72 hours. The most common cause of symptoms after this period are the postoperative narcotics that a patient takes to control pain. I hope that this answers your question.