#1
I know everyone says Amon Amarth is just melodic death metal with viking themes, and I agree to that. But before the "With Odin On Our Side" album, which is the album most people have heard, they had a pretty viking metal sound. If you listen to the really old albums like Versus the World, The Crusher, and Once Sent From the Golden Hall, they had a fairly black metal sound. Not theme-wise, but the vocals had more shrieks like the song Arrival of the Fimbul Winter. Yeah they occasionally (although rarely) have solos, so do viking metal bands. Einherjer has a number of solos. I think the reason most people would say they aren't viking metal is for their newer songs that are more melodic and deeper growls, and the fact that they don't really incorporate clean vocals like Vintersorg, Falkenbach and Bathory have.

Anyone care to debate or speculate why or why not they might be viking metal? I mean, they've shown a number of signs of viking metal sounds on their older stuff.
#2
I consider them melodic death/viking metal. Their older stuff is actually closer to Melo-death than viking metal IMO.
#3
Viking Metal is one of the less prominent sub genres that is hard to specifically define...

So don't worry about what makes them viking or not, and just be thankful that they're making some good music...

-TFA