Vaguely, I remember camps that were waterless, but that there were some creeks and decent water sources so that I didn't have to carry too much water. I'd suspect that spring is a good time of year for water.
Not sure that I had a permit when I went. I don't remember it.
I'd think that spring is one of the more popular times to hike it, but that likely if you look now there would be spaces.
I've been out there multiple times, but the time I backpacked it, in November, I saw no other backpackers.