Hey quadro,
The first thing, about songs in the wrong key isn't all that uncommon. Back in the baroque period there was even a whole phase in music in which keys were thought to the ability to provoke a specific involuntary emotional response - D major is joyous and so on. This school of thought is known as the Doctrine of the Affections. It isn't really given much credit anymore, but I bring it up to say that we have known for a while that the ear is very sensitive to pitch even when the brain can't recognize it. Meaning that even if you can't name the key you know that it isn't right. With the singing thing, I can sort of do that too, but a lot of it is because I know from the physical sensation where pitches lie in my voice. Like E flat below bass clef resonates in the bottom of my throat, near my chest. Like I said before, even though I can get pretty close to finding pitches with my voice or name them on an instrument that I am familiar with, I can't identify them from just any sound. More importantly, likewise I can't "prehear" them in my head.
My feeling is that the brain can accept a ton of information from the ears - it can accept way more than it can process. Some people are wired to recognize pitch without reference and some aren't. However, the brain is very canny and can use other clues, like timbre or recognizing the sensation of singing to clue you in. This realization is unconscious though. In music schools you typically have to take a few years of class called ear training. Through listening to piano and singing exercizes they teach you to process pitch more consciously. It is really important because a conscious process is a repeatable one, so if your heart is pounding and your mind is racing from nerves your sense of pitch doesn't crap out on you as well.
By the way, I just noticed that you are in NY - awesome, me too! (which you probably did see before)
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Cogito ergo spud -- I think, therefore I yam
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