Instead of useing anesthesia for surgery is there any other options?

What kind of surgery. Types of anesthesia are local light sedation by rn; deep sedation, nerve blocks, spinal, caudal , epidural and general all by anesthesia providers. None of these is always the safest and each one may be the safest for you depending on your medical condition and type of surgery. I would not use any other things like hypnosis or acupuncture for any surgery.
No. In general it depends of the surgery. There is local anesthetic (think getting stitches or a tooth pulled) IV sedation (colonoscopy) regional anesthesia (epidural) or general anesthesia. There is always the option of no anesthesia, but for many procedures that is not an option.
Depends on surgery. We cannot answer this question without knowing what operation is planned. There are many different anesthesia options including local anesthesia, twilight (sedation), nerve blocks, spirals, epidurals, or general anesthesia.
Local or regional. I assume you mean general anesthesia - its always a good idea when having surgery to go with local or regional anesthesia if at all possible. Local or regional today is very safe and reduces the risks and possible side effects of general anesthesia.
Talk to MD. There are some operations that are done without anesthesia, but i need to know which ones you are talking about before i can be of much help.
Yes. It depends on the kind of procedure, many kinds of anesthesia and some people have used acupuncture in some minor cases.