The colors did not photograph well, so please just use these pairings as templates to layout the samples I dropped off.
 
For the main walls, consider one of the following:
7641 Colonnade Gray
7570 Egret White
7672 Knitting Needles
7647 Crushed Ice - the coolest option
7634 Pediment
6070 Heron Plume
6262 Mystic Mauve - the warmest option, the most unique, and my personal favorite
 
For the bedroom (neither are as yellow as they appear in these photos, they're green)
7732 Lemongrass
7733 Bamboo Shoot
 
Options for the workout room. Blues are calming, so I would recommend painting stripes using one of the greens above and one of these blues. To lighten the space, incorporate your main space color, as well, and create a trio of various size stripes. Vertical stripes make a room feel taller, horizontal stripes make a room feel like it has more square footage. I've added a few example images to this folio.
6237 Dark Night
6243 Distance
 
Barn Door Options, both of these add warmth and will tie in with natural wood pieces, such as the live edge bar:
7048 Urban Bronze (SW newest color)
9175 Deep Forest Brown
 
Bathroom Options:
6237 Dark Night
7641 Colonnade Gray
7570 Egret White
7672 Knitting Needles
7647 Crushed Ice 
7634 Pediment
6070 Heron Plume
 
Study Area & Long Hall with wall mouldng:
6237 Dark Night
6243 Distance
 
Ceilings:
Sherwin-Williams Superpaint Flat without tint
 
Trim and Doors:
Have your contractor color match what is upstairs and use satin finish
 
Wall Paint:
Use Sherwin-Williams Cashmere in Low-Lustre
 
There are lots of mix and match options here, however, Mystic Mauve is not likely to work in the bathroom. I like to add a bit of interest and drama to a windowless bath so personally, I would use Dark Night (assuming it coordinates with the tiles).
 
I would keep the lighter blue and lighter green together (Distance and Lemongrass) and the darker two together (Dark Night & Bamboo Shoot). However, that doesn't mean you can use Dark Night as accent elsewhere, such as the backs of the bookshelves and the long hall wall.
 
Basements can pull toward the cool spectrum and blues are a cool color. To create a sense of coziness and warmth, the blues here have an slight undertone of red (Distance) and green (Dark Knight). Green is a neutral but works here because of the yellow undertones.
 
Typically, fitness spaces have a color that will provide energy, even if it just used as an accent color. Blues and Greens are both calming, and cooling, so while they may help you believe you're not getting as hot during your workout, they may also slow your rythym and motivation. That's why I suggested stripes, which provide energy (and a little interest and counterpoint to other walls down there). If you're not a fan of stripes, we can add energizing contemporary art with reds and oranges.