#1
I was just playing around and came to an idea. Say you are playing around with two notes at a time. Start with a minor third and play around, stay in key, and finish the song with a major third behind that beginning minor third and slide up to the minor third e.g.

g 4/5

D 5/7

would you say that the song is in C major or A minor? I am not sure because there is both a resolution to the A and the C while the A is the bass note, but the C has the strong half-tone resolution, making me unsure of what it resolves on. Say I add an E into the mix, on the b string, how would that change it?
#2
unless theres other instruments doing other things that might alter your harmony, with thirds i believe its usually accepted that the root is the implied chord. so there, you're basically going G - Am, VII - i. pretty common minor movement, so it does fit into A minor. and adding and E note to it would only make the A minor sound stronger, you'd be forming the full A minor chord: A C E