Questions:
1) There are sites where you can look up historical weather data and you can see all the time high's for say Ely, or Eureka, but the length of 50 has a baseline of around 5000' of elevation so you are probably not going to run into extreme heat. And if you do, just start out at dawn and wrap up your day early.
2) Never having been to Nevada before that tour I couldn't have imagined what I saw. Not a house, not a fence for miles and miles. There is a periodic pull off you'll see and you could camp there but you will not be sheltered from view so you won't be very stealthy but I don't know that its illegal to camp alongside the road. Maybe someone else can clarify. I stayed in hotels.
3) In September there was no, and I mean zero surface water, but there may very well be some snow at the higher elevations when you go thru in May. Having said that, there's definitely an ethic in the rural west that if someone is in trouble you stop and help them out. If you ran out of water or had some other emergency you can flag down a car and someone will stop.
I'm making this sound pretty grim but the miles on 50 east of Fallon to the border w Utah were some of my favorite miles of any of the 6 long tours I've taken. There is something mesmerizing about that place, like you are riding thru another world.