I dunno if there'll be a question at the end of this, as I am in rambling mode, and this is just an observation, buut...

I've noticed if I'm listening to a song with lots of harmonies on my headphones, then take them off to hear something else, then the higher pitched harmonies suddenly seem to jump way up in the mix; and I'll be able to hear the backing vocals much clearer than the lead.

I was wondering, is this effect from the change in volume, or just a change in where I'm listening to it from. If that makes sense.

Also! If I level everything individually, then alter the master volume level, will that change the balance of the other tracks?
"Levelled up. Still no solos."
Yes, different frequencies are perceived differently at different volumes. Look at some Fletcher-Munson curves to get an idea about it.
And to add to the mix.... your ear perceives frequencies differently based on how far away you are from them. The implication of this is that monitors need to be placed properly in relation to the listening area.

Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.