How high is the probability of getting birth defects with exposure to general anesthesia?

Very very low. We try to limit exposure to all medications during pregnancy, but there are no known problems with general anesthesia in pregnancy. The anesthesiologists follow the oxygen levels in the mother which is the most important thing.
Minimal. Of all the anesthetics that we commonly use, only the benzodiazepines have been loosely associated with birth defects in the first trimester. Discuss with your anesthesiologist your concerns and see if you can come up with a treatment plan for you.