Hm, that's a nice question! I think, it reveals to you your potential more than anything specific. The more you gain control over everything, the clearer your visions will translate into your music. Dreams reveal to us aspects of our existence that are otherwise hard to access, but present nonetheless. Oh, and I've had that, too, more than once, I think.
I once made a curious exercise while having been in an alpha state, closely around falling asleep or waking up, you know. In this exercise I attempted to hear in my mind more than one voice, accumulating a whole orchestra with choirs at once. It took me a moment but eventually I saw- in my minds eye- a vast forest landscape with low rolling hills and above them I started to hear and fully control a whole choir with some orchestral support. I couldn't hold it for very long, but it was quite amazing. With some proper meditation, I'm sure this could become fairly normal to accomplish, though.
With choirs, well, I'm afraid that you just need to have proper material, decent samples, you know. Otherwise you'd have to rely on choirs just supporting your arrangement in the background and only subtle.
As for the mix, once you are aware of the concept to keep frequencies separated for each member of your orchestration, you will automatically come to cleaner mixes. Even when you want to go unisono, with various groups playing the same melody, you will try to pick instruments that don't overlay badly, but saturate different parts of the spectrum. Sometimes there, too, octave shifts can help keeping it neat.
It's always good to have a nice analyzer displaying to you the frequency band levels in real time. It helps you to dial in proper values for the EQ of each instrument.
But there's so much more to all of this, the deeper you go.
Currently as I'm playing around with orchestration, I'm not too concerned with the mix, as I rely on the natural recordings of the samples for all groups. If I use different libraries, I'll see that I balance out the volumes, though. But I haven't really gotten to that, yet.
As for music and mathematics, well...the field of mathematics is vast and music appears to take advantage of great many disciplines math offers. I haven't spent too much time with those explorations, though, so ... it's just something I can imagine. The big trouble is that we have to bring everything into the range of general perception for a human. We respond to different frequencies in different ways. There alone are a set of dimensions worth considering. From alluring sounds to alarming sounds to internal sounds and rhythms, they all play different roles and come in their own parts of the spectrum. Some of which align to specific intervals across the spectrum...eh...worth countless contemplations and observations!

It's easy to get carried away, of course... but for now I'd just focus on detecting problems in your mix and solving them, but otherwise just flow freely. The more you become conscious of, the stronger your intuition will point you to the right sounds with the right notes!
