Cryptoconspiracy II - The Endgame for all of crypto - Bitcoins doomsday?

Having tried to wrap my head around bitcoin for a couple of years I asked myself what might go wrong?

Understanding the Blockchain Technology on a basic level, there have been two things that I could't find an answer for:

1.) How safe is SHA256, and does the NSA/FED have a finished research paper in their desk drawer to destroy it within a blink of an eye?

2.) How safe is elliptic curve cryptography and the trapdoor function? Is there a way to work around it, and calculate likely private keys from a public key? Or at least narrow down the solution space for potential private keys to an amount that a powerful computer could try to figure out by brute force within a reasonable time?

If either of those, or both would be possible could the whole crypto environment go kaput in an instant?

With an approximate evaluation of crypto of 200.000.000.000 going down the drain, the crypto,- and goldbugs would at least have to be less worried about inflation :)