1. Yes, but we ain't psychic. If someone comes up and says "I am doing this cause of God!" we can safely assume they are doing it because of God. In the same way that [i]if[/i] someone went "I am doing this because there is no God!" we can assume that's their reason. Except no one had said this, you are suggesting hidden motivations. Which although very plausible (if not most likely, everyone will have some motivations they keep to themselves) you are at no position or ability to judge or determine them. 

Is it theoretically possible for an atheist to start a violent purge of religious people because they are religious? Sure, humanity produces some very messed up people. But do we have any recorded cases (Not assumed from an absence of religion motivation) of that being the motivation? Nope.

2. More precisely, killed because they worshipped/believed something that wasn't there leader. They could have gone around worshipping their local baker and they'd still get killed. It was about praising something other than their leader, not about the fact they were religious.

3. Yea, I would. Because it proves itself to have religious motivations, but it doesn't so it's not a religion. In the same way that if I happened to believe in God that would make me religious. That's not a double standard, that's just fact. Belief/worship of a God is religion.