As to the first question, I also couldn't find that in the textbook, and was again given a rather vague answer by my professor. He said it is because if there is a problem with the system, the planes, or the people, the problems will usually show up in some way in the maintenance records, so that's the easiest place to look. As for how public complaints are handled, they are directed toward the new FAA Office of Audit and Evaluation which also handles relations with the US office of Special Counsel, the Government Accountability Office, and the Department of Transportation's Office of Inspector General.
Chapter 2, p. 47
The steps in the accident investigation process start out with the go team being dispatched, filled with people such as human performance experts, and experts trained in witness interrogation. Next is the party selection process which consists of naming the various parties (specialists) that are to help with the investigation. Moving on, the attention is next given to the accident site. The time needed at the accident site can vary from between 10-14 days, however investigations can often require off-site engineering studies or lab tests. Those laboratories (the next step) performs detailed analyses on items found at the accident site. Toward the end of the accident investigation, an accident report is prepared, a public hearing is called to collect added information, and last of all, the final accident report is published, and safety recommendations are made to the FAA
Chapter 3, p. 69-74