My question is this.

1. (for example) If A minor and c major use the same notes, how does one determine which key the song is truely in?

well, in every scale you have a home note. you have a note that feels like eventually you gravitate back to it, sooner or later. it just feels like that.

so both scales will the same sequence of scale notes, but have different home notes (tonic note). in A minor it will be A. in c major it will be C. The sound of the piece tell you that, you just listen to the piece, stay with it, and you can just find that home note.

If it feels like you gravitate to the note A, and you have the same notes as in C major, you know it is A minor.

Just think of a simple minor key song. "God Rest Ye Merry Gentlemen.....". A lot of Christmas Carols are minor. At the end, ".....tidings of comfort and Joy", undeniably, the note at Joy is the one the song gravitates back to. You just tell by the tune, it is self evident. That is the home note. It will have the same scale notes as the major key 3 semitones above it. But they are completely different scales. You might modulate between them, as they do with many scales. But they are different.

hope this helped, not sure it did though.

Pretty good explanation, F - that is one of the simplest concepts in music when you understand it, yet the most difficult to explain - you did a nice job

When playing any scale, root notes are what determine the scales key, even if they do have exactly the same notes, if you start at a different point in the sequence with a different root note, you will end up with a different sounding scale, but that is hard to hear because you are using the same selection of notes.

The only way to really understand this is to compare like with like. In your example, you want to understand the difference between a minor and a major scale, so compare C major with C minor. or A major with A minor - only when the root notes are the same can you really hear the differences at first. Later on, you learn to assume the root note in your head, but that comes with practice and experience.

Either you gotta recognize the chords, or simply *hear* the quality of the song. does it sound light and happy? major?
Sad? minor? funky? dorian/mixo perhaps?

Hope this helps