There is an issue beyond fill: there is a limit on how many "current carrying conductors" you can have in the same raceway (conduit) assuming it is over 2' long.
If the insulation is rated below 90 degree centigrade, the limit is three current carrying conductors.
For thhn or thwn, the rating of the insulation is 90 degrees, and the limit goes up to six conductors.
If you need more than that, one gets into derating calculations, and the ambient air temp that the raceway is in is also calculated. It can get quite convoluted.
All that said, I have never considered the matter with NM.
You are running a lot more circuits than needed, I think. You only need one dedicated 20 amp circuit for all the bathroom outlets, but they should serve no other purposes. Some will say you can hang bath lights and fans on them, I'm not so sure.
Mike Holt has a free calculator if you go to his site: http://www.mikeholt.com/freestuff-menu.php look at "residential load calculators".
A sub panel is a VERY GOOD idea. Do not put it in a closet or a bathroom. Put it behind a bedroom door where it will not be on view very often. You need two hots, a neutral and a ground. The ground can generally be one size down from the hots. Don't forget to keep the neutral and the ground separate in the subpanel. And the hots must be correct colors, the neutral must be white and the ground must be green.
You can get non metalic in 6-3, although it will cost a fair bit. It would be just the thing to fish up your plastic conduit, just treat it as you would any NM when it passes thru a stud.
As for general purpose circuits, I am just a tyrant against making them 20 amp and using 12 ga.
There is NO reason to do so nor any advantage. 15 amp with 14 ga is perfectly adequate and lord is it a lot easier to stuff the wires into the boxes.