Can I be signed into iTunes with a different account than iCloud on same iPhone at same time? Can my iTunes &amp; App Store account  be separate from my iCloud, Messages,and FaceTime accounts? 
Can I be signed into iTunes with separate account from iCloud, iMessage, etc, at the same time on the same iPhone? 
Can I have a separate account (Apple ID) for iTunes purchases than my iCloud account?
Yes that is what I have.

I have this because my iTunes account predates apple mail and backup which are the predecessors of iCloud. The latter had to be a @me.com address and my iTunes account was not. The usual problem is that Apple has not provided a way to combine these accounts for those who want to. 

Your could have a third email with Apple for development membership. And your iTunes login could differ from your Mac apps store login but that gets too confusing.