How did teen child tolerate having teeth removed?

Depends. Every teenager is different. However most are compliant and listen to the doctor. If non compliant, then laughing gas or sedation can be considered.
Depends. Every teen child reacts differently when in a dental office. Some children undergo extractions only with a local anesthetic, some with oral sedation and local anestheisa, some with nitrous oxide (laughing gas and a local anesthetic) and some require a general anesthetic.
How many? How many teeth are you talking about? Sometimes kids need to have a few teeth removed in order for the others to be aligned properly with braces (if there is too much crowding). Generally, it is a simple procedure (my son tolerated it well).