How likely is it that an underweight adult going under gen anesthetic for teeth extraction, will die/have awareness?possible heart/lung problems?

Vey unlikely: There are various levels of anesthesia, and the risk depends on the level of anesthesia. However, intravenous anesthesia for tooth extractions is extremely safe and carries a lower mortality rate than general anesthesia for other procedures. If you're young and healthy, you should not have any heart or lung problems. Whether or not you have any awareness is a function of the level of anesthesia.

That depends,: In general the risks you ask about are very small, however, complications from gen. Anesthesia would depend on how underweight you are and how healthy you are in general. I would suggest you first seek medical clearance from your primary care doctor and then review your concerns with the anesthesiologist in advance. They can better appraise your specific risk for complications.