Decay chains are probabilistic. However, that's what's so good about Thorium: a different set of decay chains, with a lot less trans-uranics in them.
Wouldn't happen. All modern designs Fail Safe: if the fuel melts without coolant, it falls out into reservoirs, each too small for the chain reaction to be sustained.
We actually learned something positive from Chernobyl. Uranium fuel forms a stone-like muck (called Corium lol) which slows down its reaction. Chernobyl certainly melted down, but the ecological damage happened before that, with the explosion and fire (chemical fire: it used graphite as a moderator). It's pretty much stable now. Nobody is talking about building more reactors like that, it was a false economy of a very large pressurized moderated reactor, designed to use (cheap) weak fuel.
Sounds quite reasonable and balanced ...
Short term waste can just be stored short term, and it dwindles away. The very long term waste is similarly harmless (in fact most elements in Earth's crust include some long term radioactive isotopes). It's the medium term and short long-term 'transuranics' which have to be securely stored. These are much less of a problem (so far as we know) with the reaction products of Thorium. But they can also be recycled into new fuel (or lesser radioactive waste) using a fast reactor. The French were working on a full-scale fast reactor when it got shut down by ... if you can believe it, a greenie with a shoulder-launched missile.
Personally I've given up on fast reactors, they are cemented into the public consciousness as Bomb Makers (they do in fact produce Plutonium). But chemical separation works, to separate the worst waste, which can then be stored somewhere with stable geology. Now someone will start speculating about asteroid strikes, and we're back to justifying the safety of a technology which even including ****youshima and Chernobyl, is safer than fossil fuels and safer than rooftop solar.
Or we could stop calling Fast Reactors that. "Recycling reactors" sounds better hmm?