I would saaaay... the 12v applied to a 5v strip blew the hell out of all the 2811's. The 2811 at the front failed such that the data in pin was shorted to +12v (often when you fry a chip it's I/O pins get near-shorted to vcc or ground). Then the +12v applied to the data pin trashed the arduino. A 12v 2811 string is bizzare and probably doesn't actually exist - the chip wants 5v, and since they're individually addressable, it's not safe to put them in series (as the load on consecutive leds may not be the same). Unless it's got a switching power supply to convert 12v to 5v at the start of the wire, you hooked a 5v strip up to 12v. To be fair, I would totally believe you if you said a chinese ebay vendor said it was 12v on the product page. I think there's a different addressable led chip that does work at 12v (2801 maybe?), but not 2811.
People often have issues mixing cheap chinese PSUs with other equipment, e.g. powered by USB. I suspect it is due to grounding issues, possibly even that +12V is referenced to ground (verified by one user).
That problem could be avoided if you take the 12V and convert it to 5V for the nano with a suitable voltage regulator.
I think it was due to grounding as I did not have the wires soldered. I will try again but I was wondering if it is possible to power the Nano using the 12V. I read that the VIN can be used?