>What about all the nuclear waste that is already building up and has no where to go?
The design that Bill Gates advocates would use this exact waste as fuel [1], or more precisely the long-lived isotopes in the waste. The remaining isotopes decay by themselves in relatively short time (years, decades, at most a few centuries).
> There was a incident where a employee thought it would be a cool picture if they put the rods next to each other. They were literally lucky that it didn't cause an uncontrolled reaction.
I remember reading about some incident like this. I don't believe the stuff though. If it was that easy to create an "uncontrolled chain reaction" it would be very easy to build a bomb. You wouldn't need an entire Manhattan project to do that.