Less than you'd expect but more than today. A trial by combat was very much the exception, not the norm.

But swords and the ability to fight were status symbols, they expressed power, authority and privilege. First and foremost of nobles and knights but also of other social classes and authority figures.

That has to do with the feudal class system. Generally, in the very broad strokes, serfs didn't have the right to wear swords, but they also didn't have the duty to join the army in case of a war. Free people could be drafted but they had the right to wear swords. That was very important to the craftspeople and merchants in the big cities, especially since there wasn't such a thing as the police yet so knowing how to defend yourself was sometimes a good idea and sometimes legally required. Wearing a sword meant "Look at me, I'm free and proud of it. I can afford a sword and I can and will use it on you if you give me a reason to."

Not much at all. Swords were tools. The single most common one was the falchion, aka machete, owned by probably every farmer in Europe in one form or another. It was also the most common battlefield sword, used by nobility as well.

Generally, other than a belt knife, the wearing of weapons when not "under arms" as a watchman was limited to travel, and even then not always, depending on the size of your traveling party. The medieval world wasn't nearly as violent as most people think; a simple walking stick or staff was usually more than enough. The idea that everybody was armed and armored constantly is a modern invention.