Our basement has a little natural light from 2 small windows. Had leveling compound poured and then installed laminate flooring (a very light natural oak color) over the concrete. Huge difference. Huge. Made the room much seem much brighter and twice as spacious.

You have a walkout basement with lots of natural light, so it wouldn't seem a problem. But I confess I prefer dark floors to light ones anywhere--except for a small space with light walls where a dark floor would emphasize the smallness of the space. I would avoid using any vinyl directly on a basement floor to avoid mould problems. See this thread for some further comments on basement flooring.

I'd prefer that more grout had been left in the joints. They look dished out a bit too much, where too much grout was removed during the cleanup phase. I'd have preferred the grout to be more flush with the face of the tile. Looking closely at the first two photos, the darkened grout lines are all parallel to one another. In the first photo you can see the wet grout lines are all parallel to the edge of the drain. That leads me to believe that the "uphill" edges of the tiles are acting like mini dams and holding water, they are preventing water from easily flowing downhill to the drain. The second closeup photo, you see the same effect. All the damp grout lines are again parallel to one another. Again, to me that reflects a drainage issue. Not necessarily with the amount of floor pitch, but with the grout lines being so dished out that they hold water and slow drainage. Marble is porous and can absorb water. With the grout lines being a bit too raked out, the edges of the marble hexes are exposed. Water held against the tile edge can lead to absorption into the marble. The crack in the grout in that second photo, you also wrote that there are other cracks. That's usually a sign of too much water used in the grout mix, or that sanded grout should have been used instead of unsanded. Unsanded should be used in joints less than 1/8" wide. Cracks can also indicate movement in the floor, but that shouldn't be an issue with a properly set Kerdi Tray. As far as him having used a preformed Kerdi-Tray, if he did, it appears that is was certainly cut down in an awkward manner. The drain is no where near centered in the shower. So if he did some filling here and there with mud or thinset to even out the floor pitch or edge elevations, that could have be part of the problem. But that's supposition on my part. About the only other thing I could question is that often times with small tiles, when the sheets are set into the thinset, thinset can ooze up between the hex tiles and partially fill the grout lines. That thinset needs to be cleaned out so the grout lines can be completely filled with grout. If it's not, you can get uneven thicknesses of grout, think of it as a veneer of grout over a blob of thinset. That can result in uneven water absorption, the grout cracking, etc. All that aside...with this being your second go-around, he should have install the sloped Kerdi Tray and thinsetted it to the subfloor. Then he should have set the Kerdi drain. Then he should have thinsetted Kerdi Membrane (an orange colored sheet material) over the Kerdi Tray, then tiled on the Kerdi Membrane. I'd be interested in how he tied the Kerdi Membrane in with the wall membrane IF he used Kerdi Membrane over the Kerdi Tray. Best. Mongo

Is the floor concrete? Are you looking at epoxy paints designed for concrete floors? My ex did the garage and it looked great (don't remember what brand he used). What are you planning to use the room for? If it is work space (craft room, shop, hobby room), white or light color might be best, since you'll want to maximize light. If it is going to be a TV room, you could go with something darker and more intimate.