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Sorry to hear about your issue, but it sounds like you're learning a lot!
When my old 08' 135i w/ PPK was around 100,000 miles, I realized that nowhere in the textbook-sized service and warranty records had the spark plugs been replaced (ouch!). I then went on to find one stuck plug.
Unfortunately, there is no risk-free fix for this. A relative who works as a BMW service advisor recommended that I just leave the old plug in there until it failed.
I'm more stubborn than I am a can-kicker, so I tried an overnight PB Blaster soak. This didn't work, so i dried out the cylinder head with compressed air and paper rags wrapped around a skinny flat-head (make sure it's dry so as not to ruin the coils!). I drove the car close to home until the oil temp gauge barely had a reading, so it must've been about 160-180F. Water temp (which warms to operating temp faster than oil) would be more useful since we're dealing with the cylinder head, but all I had was the oil temp gauge. With a little heat in the engine and a prior-night PB soak, the plug came out without feeling like I would break something.
As I said, this is not risk free. Heating the aluminum head to expand more than the harder spark plug makes the threads softer and susceptible to damage. This is why you only want to warm it up, not bring it all the way to operating temp. In theory, this approach is relatively safe because machining standards of heads and plugs should be precise enough to discount an obstruction in the threads other than ordinary carbon buildup, and twisting carbon buildup shouldn't wreck a warmed-up head. However, if the plug is cross-threaded, this approach will tear up your threads. I did not have this concern since my stuck plug was factory-installed, but you do have to consider this possibility. Cylinder 2 is not particularly hard to access and is less-likely to be cross-threaded than other plugs you already got, but there's still a chance.
And if you do this, let the head cool completely before installing the new plug. You don't want to torque the new plug in a softer, heated head because then you'll be back at square 1 in 50,000 miles.
Good luck!
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