Its also possible that he might be in one of the Mirrors of the wheel, which diverged from the main world after the Last Battle happened. That Mirror could be close enough to have the people, and maybe is closer to TAR so that the thinking ability is present, etc...
Its entirely possible that the Chosen built that structure in their heads - 'I did something good, I should get access' or 'I'm the only one left, I should get access' or 'so and so said I did good, and has given me access'. TDO certainly never 'granted' Rand access. Rand took it. Which means...
As far as the impossible pipe goes, I think that the dragon has always been one of five things that can stand outside the pattern. The Creator, TDO, TAR and TDO's champion being the other four. You'll notice that Lanfear, (who I believe was TDO's champion) had the ability to do many things...