Heh, somehow I didn't notice the question at the end of your post until now. Eh... well, it would depend on the context, really, but in regards to the "thinking" referred to in regards to "can only think of one thing at the time", I guess my definition would be along the lines of... "can only run one process at the time" or "can only follow one train of thought at the time without consciously switching between them", though I'm not even entirely sure how I feel about the latter. I guess when I say "think about *blank*", I mean "process *blank*".
So I guess by my definition, thinking can be a is all complex analysis.

And I got what you meant in regards to the way I recall/hear music, and that is what I meant. I, uh, apparently work in horizontal layers? I also very rarely have any trouble separating one sound from another (unless one is significantly louder than the other to the point where I actually have trouble hearing the one I want to separate) and am practically never distracted by sound per se. The only time multiple sounds can really start to confuse me is if there are multiple layers of sound that I feel like I should pay conscious attention to (most notably, if multiple people speak to me at once; I actually find it particularly confusing and downright disorienting when that happens). When I listen to music in real-time I have no problems shifting my focus from one layer - the vocals, for instance - to another - like a particular instrument - and sort of "fade out" the rest.
When I still played Battlefield I remember usually doing pretty well, because even with a cacophony explosions and gunfire everywhere, I still never had trouble registering footfalls beneath it, which in turn meant that no one could manage to sneak up on me (unless they were actually sneaking, but everyone sprints in Battlefield). So I guess I just naturally separate sounds into layers? Heh.