Well I'm of two minds on the whole 10 Rings - Mandarin thing
1. There WAS a "Mandarin" leading the 10 Rings originally - but AIM somehow killed him and basically replaced him with their own man and just co-opted the original 10 Rings
2. 10 Rings was always meant to keep Stark - it was the guys in the field, like Raza (Robau!!!!) who sorta fucked things up and got too greedy in their own fight - like 10 Rings was Killian's invention but others that joined it and created cells sorta were on their own - but as I was saying, they were always meant to hang onto Stark once he gave them the Jericho missile - since THAT particular cell wanted it. The terrorists that captured Stark were surprised that it was actually Stark and wanted more money remember? It was Stane that sicced them on Tony. Which is how I'm sure the whole Afghani group that Raza was with got to California pretty quick - if they were part of Killian's 10 Ring.
3. The 10 Rings IS a real terror group in the MCU that Killian was using for his own end and figured if anyone from them went after him, he'd sic Extremis guys on 'em. Like say, someone using one of the other known terror groups and doing things in their name, the group thinks 'uhm okay hey you're doing alright... welcome aboard' but it's all a ruse.
4. Killian didn't care of Tony lived or died, he wanted Stane in charge so that he could ramrod Extremis through SI saying 'okay we took care of your problem Stane, now take care of mine.'. After all, he waited a little while for Pepper to be fully integrated into SI before approaching her.