It depends on the jurisdiction.
1. Generally, if someone calls 911, their call is not anonymous. They are asked to provide their name. That is the first thing the operator asks, before the emergency is reported.
Even if they don't provide it, the emergency operator automatically has caller ID. Most 911 calls are made using a cell phone, so the operator automatically knows the cell phone number.
People call 911 for a great number of reasons. A great many people call 911 when they are very distressed, so they often hang up before they have given the operator enough information. Like if they call to report a fire, it might be a small fire (1 truck), or it might be a very large fire (multiple trucks). People very often mistakenly call 911 for non-emergencies. The operator MUST therefore be able to call the person back.
2. It is complicated. In many locations, the unconscious person will be billed, but in a number of locations, if it was an emergency situation, then the government pays for it, or pays a portion of the cost. It has to be an emergency though. The amount owed might be the full cost, or it might be a % split, or it might be something like a $100 or $50 fee.
B. If the person is unconscious due to an auto/insured vehicle accident, the auto insurance might pay.
C. It is even more complicated than this though.