Why do the people on the emergency line sit there and ask you questions instead of sending an ambulance during an emergency?

Although you may not realize it, they have probably already dispatched the necessary first responders while you're talking to them. The questions they are asking are to assess the seriousness or nature of the problem, which are factors in determining what type of response is appropriate, eg: 1 ambulance or more, police? fire department? how many trucks? what type? Additionally, information they get during a continued contact can be passed to the emergency responders enroute, thereby allowing them to be better prepared to meet whatever challenge awaits them at the scene. The continued contact and conversation with the reporting party helps to reduce panic or anxiety in the caller, and thus helps to maintain control [albeit remote] of the incident scene until arrival of the first responder[s].