Re: Ten rings to rule them all...
That's the thing --- I think the rings *do* have powers, but they're not magical or alien. They're (Extremis) nanotech.
Your theory about Killian giving Mandarin the source code to control Tony's Extremis armor makes sense, too, but I still think that's a case of the armor becoming sentient, as we saw in that story arc in the comics back in 2000 or so.
I've not been keeping up with all the tiny details that differentiate each MCU armor from the other, but can someone who does tell what model that is that shows the sentience --- i.e., the one crouching over Pepper, and later over Stark? To my untrained eye, it looks like the original one from IM1...
THE COTTON AVENGERS
...They move like slick cotton on oil.