Does load factor limit actually change with aircraft weight?
Yes, the limits are always set by the worst combination of weight, loading, flight speed and expected gust speed. They are valid over the full range of parameters for simplicity reasons.

Note that the load factor limits are not directly proportional to the aircraft's overall weight, but the weight of the non-lifting parts. An empty fuselage and full wing tanks allow the aircraft to pull more gs or fly faster until the maximum wing bending moment is reached when flying through the maximum expected gust. Calculating the precise load limit during each stage of a flight would put excessive demands on any pilot and increase the risk of errors.

All components should be sized so that they fail at 150% of calculated maximum loads. In real aircraft some secondary considerations like the availability of sheet metal gauges or extruded profiles put a limit to this local optimization, but technically the chance for breaking is the same for all structural parts. All the failures described in your question have happened in the past when aircraft were overstressed or improperly designed.