I didn't know the first two, but they may not have made it in the UK. I do like NIN though. Not seen them live.
I think the US and UK 'alternative' scenes had some differences, but there would be some overlap. It can cover just about anything that isn't pop or some other major genre, but tends to involve guitars. Some bands defy being put in a genre.
Yeah, I would agree with that. I think if I had to put a term to it I would say that the UK alternative scene was a bit more ethereal than the US.
I just don't think you can generalise. Just see the variety that @slobberchops put in his #AlternativeWeekend posts.
It depends on the era. I stand by my statement if you are comparing something like grunge to alternative music from the UK at the same time there is something brighter about the music from across the pond. If you are talking about something like The Smiths though, totally different feel, but also totally different era.