Yes, Han was referred to as General Solo in ROTJ. If the war continued for another year that likely was not his only action as General and he would have become quite famous for that. It is not surprising that Finn, as a stormtrooper, would be aware of his Rebel Alliance history.

Just as it isn’t surprising, considering the sort of people she lives around, that Rey would know of his smuggling fame.

As for the “Kessel run in 12 parsecs” line from ANH, it makes a lot of sense when you consider other dialog in ANH. A powerful and fast ship could get closer to large gravitational bodies and shorten the distance of a run through a tight hyperspace route. Stars and planets are navigational hazards in hyperspace so being able to get closer to them might give access to a better route that would shorten the distance. On the surface it seems silly if you know that a parsec is a unit of distance, but it isn’t that ridiculous when you consider that 1920’s road construction led to longer distances than modern roads. Many roads have been realigned over the years to provide shorter distances through uneven terrain. I think Han’s explanation to Luke about Hyperspace really explains why a distance for the Kessel run means the Millennium Falcon is a fast ship. I liked the joke about 14 instead of 12 for Han’s record.