Breeder reactor:
A breeder reactor doesn't actually create new fuel but it converts urqanium 238 in plutonium 239. The first one is not fissionable by itself, you can pack as much as you want, it will never sustain a chain reaction. Bombarding the thing with fast neutrons can produce plutonium 239 that is fissile. When you have enough of it, it starts generating enough neutrons that it sustain a chain reaction, thus producing energy (see A-bomb too) that can be harvested for useful purposes.
The same could happen with thorium 232 in uranium 233. Uranium 233 is said to be fertile, it doesn't fission like plutonium 239 but it can be easly transmutated in U238 and then P239.
With a breeder reactor you start with a batch of "standard" fuel and then create the others in the reactor. (remind that low enriched uranium is 97% isotope 238 and only 2-3% isotope 235.
Second: the slugs remaining after the recycling processes are quite radioactive, being encased in glass makes them inert (no chemical reactivity) then to shield people from the radiaction they are encased in concrete and iron casks (dry cask storage) and kept there till radiaction levels have diminimished. (even 1000 years - that's why i like transmutation and reprocessing!)
The cask are extremely strudy! The walls can be up to 2 metres thick (6.5 feet) and because the fuel is a solidified glass it doesn't leak nor interact.
The organic solvents used in the recovery processes are cleaned and recycled in the cycle, also the nitric acid. Nothing is left in the enviroment. If something like that would happen it would be a pollution disaster. Not a nuclear one!
Ohhh, I forgot you still never saw my face! So here I am. Inside the RB-3 reactor at ENEA in Bologna!!!

(yes, that thing I'm in is the empty vessel)
