Hmmm. Not quite sure I follow your latest question, Mrrzy. As far as the songs you listed, someone who had those specific recordings could tell you what key each used on that recording--I believe that's what you're looking for. (Sorry I can't help you there.) In the greater sense, any song can be done in any key, so it's not that the SONG is in a given key, but the RENDITION is in a particular key.

The "switching octaves in the middle of a song" thing you described above tells me that you're singing along with a rendition that is in the wrong key for your voice. If you want to sing along with a particular recording, you're stuck. If you want to sing along with a recording, you might be able to find a rendition by a different artist using a different key. If you just want some accompaniment, you may be able to find a musician friend who could accomodate you in an appropriate key for your voice.

My impression is that virtually all popular music (of Western civilization) will use only the notes of our musical definitions and standards. This means that the notes of any song, regardless of key, should be there on the piano keyboard. Certainly, if the note is or is not there in one key, that same note correspondingly will or will not be there in any and all of the other eleven keys. If you're finding it's there in one key but not in another, there is some fundamental problem with consisitency in singing the tune--the key and/or the starting note simply does not affect that.

I was told that unaccompanied choirs tend to unwittingly go increasingly flat as they proceed through a song. The simplest way to avoid this is to have instrumental accompaniment. Perhaps a helpful musician to accompany you while singing would solve the problems you encounter.