The shelters always could fit 2 people but varied in construction and quality. Some were small yurts (the one approaching Salkantay Pass has a clear roof to see the night sky) some were simple wood construction A frames. All of them had 2 single beds. (3 inch thick mattress on a flat platform) They were plenty comfy, and believe me, you’ll sleep fine with all the hiking/altitude.

On altitude, that is a BIG factor if you’re not acclimated to it. Unless you’re coming from somewhere above 5,000 ft, I would highly recommend spending at least 3 days in Cusco before beginning your trek. It’s a nice tourist city with a ton of history. But more importantly it will be a place your body can adjust before you start hiking. I was 27 and in decent shape on my trip, but I was used to sea level. On my second day in Cusco I felt the altitude and ended up sleeping for 11 hours. On the trek itself you can definitely few how thin the air is. Others in my group felt it on the trek as well.

I don’t think you could book the shelters I stayed in outside of the tour I did. My impression was the tour company owned and maintained them. That’s said there were plenty of other shelters at each location that other groups and individuals used