Very good questions and there's a wealth of information to discuss with your questions. I will try to answer them briefly with a good overview as much as I can so that you have a general idea and feel free to ask more specific questions as they pop up.
Also, you may want to post this question in the Oral and Maxillofacial Surgery section as the oral surgeon is particularly adept at handling dental abscesses and the more serious consequences of such.
1) There are several different types of abscess but the most common is a periapical abscess in which there is a cavity in the tooth that invades the pulp of the tooth. The bacteria then travels down the pulp into the jawbone and begins to destroy the jawbone. Another type of abscess is a periodontal abscess in which the periodontium (the ligament and surrounding bone holding the tooth in the jaw) is infected and the bacteria can spread down the ligament and into the jaw or spread into the gums themselves.
2) If there is an abscess and it is treated, it can be fixed or it can result in a scarring of the jaw bone. The bacteria enter the jaw and will travel the path of least resistance. If it can manage to break through the jaw bone and exit out of the gum, then the person can live with an abscess for years because the pus buildup in the jaw will leak out of the "gum boil," thus reducing the buildup of bacteria.
3) Which brings us to this question. If it doesn't escape through the jaw and into the mouth through the gums, it can also spread through the fascial planes of the head. These are spaces where muscles and tissues connect. Depending on the location, it can results in life threatening results. For a lower tooth, it can spread down the neck region and cause problems with swallowing or breathing. It can also travel down the neck and into the chest cavity and can affect the heart area. For an upper tooth, it can spread to the sinus and into the cavernous sinus near the brain. This can result in a thrombosis. Also, there is a possibility of sepsis (infection of the blood).
Also, as a note, sometimes these infection of the tooth can result in severe tooth pain or sometimes no pain at all. If the pulp becomes necrotic and the tissue dies, there's no nerve to indicate any pain. Sometimes patients will experience pain if they bite down on the tooth and the periodontium (ligament again) moves, then it'll send feedback of pain.
Hope that helps.