“What happens if you have a bad reaction to anesthesia?”

There are a handful of bad reactions that can be dangerous, but those are exceedingly rare. The bad reactions that are common enough to discuss include surgical pain, a sore throat from a breathing tube, or nausea/vomiting.

Depends on the reaction. Could be as little as itching or nausea up to anaphylaxis and death.
Underlying diseases also factor into the equation.

That is a tricky question because "bad reaction" can mean a lot of different things. A serious reaction to certain types of general anesthesia is called malignant hyperthermia, and is a life threatening problem. It a rare conditions that is analogous to an anaphylactic reaction to medications used for general anesthesia. This is the most concerning type of bad reaction. Other reactions tend to be associated with nausea and vomiting. These can often be treated preemptively with medications to decrease the likelihood or severity. The potential for these bad reactions are often uncovered by the anesthesiologist prior to the procedure. Whatever your concerns, often discussing these with the anesthesia team prior to your procedure can usually be addressed.