Iron Man & the 10 Rings

So I saw Iron Man 3 this past weekend, and while I felt it was a good movie in many ways (incl. the inspired twist for the Mandarin), I was left with many questions, and a couple of complaints.

My biggest question is about the 10 Rings, the terrorist group the Mandarin is supposedly running. The 10 Rings was also the terrorist group that took Tony Stark hostage in Iron Man 1. I just really wonder whether or not these groups were connected in some way, or if in its corporate way, the Mandarin repurposed branding of the original group in order to have an established brand.

What do you think? Was the Iron Man 1 10 Rings the same as the one in Iron Man 3, or did Obidiah Stane really finish off the 10 Rings getting the MK1 suit, and the Mandarin really stole their identity?

My complaints seem minor on the movie. My biggest was at the end of the movie, when he tossed his chest reactor into the ocean outside his home. The whole plot of Iron Man 2 was that device - He was dying at the beginning of the movie, the effects of his arc reactor poisoning his body. He found the designs his father passed on to him, tore half his house up to create a centrifuge to make the material for it.

He then creates a similar device to power Stark Tower in The Avengers. And this valuable device, it gets tossed into the ocean?

Ok, let's take into account that in Iron Man 1 that Tony is not a sentimental guy (he tells Pepper to destroy the first reactor after its removed), he still want to get rid of tech so it does not fall into the wrong hands. Wouldn't some nefarious person or group search the area outside his fallen Malibu home, and grab it? Wouldn't this lead to more Iron Man tech to get into the wrong hands? That, and blowing up all those Iron Man suits at the end, its not like real fireworks - those protective armor plates have to fall somewhere.....