>I think Andreas Antonopoulos said in a video that it takes about half a billion dollars to fool the blockchain for 10 minutes. Even though that's a lot, if certain actors (state or otherwise) got interested enough, wouldn't they manipulate the chain at critical moments for their advantage?

That's out-of-date now; the total computation power of the Bitcoin network is 25,824,939.77 GH/s. It would probably take a lot more than $500 million now.