It's important to Americans because it's been sold to us as a fictitious part of a national identity. The gun industry has very successfully crafted this narrative, to the point where so many people take it for granted now, but it wasn't always this way; this is a thing that developed in (depending on age) some of our lifetimes.
Here's a book that takes a closer look at how guns took on this sort of mythic role -- more special than other tools and appliances -- in American identity:
No, and until 2008's Heller vs DC decision, private gun ownership was not considered an established right. America's status as a gun-loving nation is a relatively modern invention, and entirely one devised by gun manufacturers. It's working, too (and with somewhat predictable results).