The waste issue has already been solved. You turn it into glass then store it somewhere geologically stable, such as Yucca Mountain. See http://www.phyast.pitt.edu/~blc/book/chapter11.html
Yes, but the solution isn't to store it. The solution is to reprocess it. That's what all the other major nuclear-using countries do. The only reason the US doesn't is politics.
We have a political problem now, not a technical one... and yeah that's going to be a tough one. I wonder how long until someone figures out ways to let a 3rd world country be the deep bore storage place and allow export?
I very much doubt that'll happen. Political stability for a waste repository is going to be just as much a concern as geological stability.