Is it safe for a 2 year old to be put on anesthesia or calming gas while dentist works on his teeth? My son wont be still even if strapped.

Yes if experienced. Be sure you have someone who has training in sedation/anesthesia. Check their credentials. Ask other patients/parents who have received services from your dentist about their experiences. There is always a tiny risk in sedation on toddlers.
Yes. The pediatric dental specialist treats situations like this all day every day.
Type? It is common to be sedated for major dental work, or with special anxiety situations. It is imperative that IV sedation be done by a credentialed specialist and that cardiac and respiratory function be constantly monitored. A real time ekg must be run as well as pulse oximetry (measure of blood oxygen levels). Maxillo-facial surgeons & dental anesthesiologists. No pediatric "cocktails" to be used.
Yes it is safe. If the child won't cooperate with the dentist you will be offered the option of sedation dentistry to handle the problem. This is a very safe thing to do, but it is your choice as to wether it should be done. You have to weight the risks of anesthesia, which are minimal, against the result of not treating the cavity. Good luck.