Why are Hazal Authoritative?

What produces Halakhic authority? Was it the acceptance of the Jewish nation that created Hazal’s authority, or was it the other way around: recognizing Hazal as the experts in Tora, the Jewish nation naturally accepted their guidance? What of more recent Halakhic works such as Rambam’s Mishne Tora or Shulhan Arukh: are they authoritative, and if so, why?

(Parts 1-3: old. Parts 4-5: new)

Old version, Part 1
Old version, Part 2
Old version, Part 3
New version, Part 4
New version, Part 5