Usually I believe icons to the right are system app icon's so are you sure something isn't syncing? I have Gmail sync turned off in my account settings, but catch the phone still syncing and delivering me new Gmail emails. So there's that too.

 

I use aqua mail too and see it popping up every now and then, then when I do it's followed by Gmail alerts.

 

I think your phone is backing itself up.

 

Well I have a different device than you but when I start the backup process on my HTC One M8 the icon on the screen is identical except it's moving. The icon on the status bar is different though.

 

Its priority in interrupt mode meaning only calls and notification are allowed.

 

That's definitely the gyroscopic indicator icon, simply rotate your device 360° anti-counter clockwise and you're all set.