1024 bit keys are endangered? Only in some broken encryption schemes. You can't even break 256 bits, as the number of possibilities exceeds the number of atoms in the universe.
You're comparing keys from two different cryptosystems, which is a mistake. A RSA key ("1024 bit keys") needs to be longer than a AES key ("256 bits") to provide a given amount of security, since more conditions are placed on an RSA key in order to get its favorable properties.
When you pick a key length, you want it to be long enough to provide security for your communications as far into the future as practicable, and the classical efforts to break RSA are getting uncomfortably close to 1024-bits. Maybe in a few decades it would be practical for some adversaries to break even perfectly made 1024-bit keys.
However, I'm not a cryptographer, so someone please correct me if I'm wrong.
I mentioned your first link, the factoring of a 768-bit RSA key, in my first comment. RSA isn't a "broken encryption scheme": it's a perfectly fine one. It's just that you need to use key lengths long enough to defend against the computing power available to current and expected adversaries. That paper is just a demonstration of modern computing power, which just shows that you should use longer keys.
Your second link has garbage sensationalized headline. It actually describes a side channel attack that has nothing to do with cryptography algorithms. It's basically equivalent to a clever way of looking over someone's shoulder.
They'll all break eventually ;-) — We know that, that's why encryption progresses. The question is only: How fast do we have to progress in the future?
The issue IS not 256-bit it is the password you used to encrypt it with. Using letters, caps, symbols and numbers with 12 that would be an incredibly large budget to get your password.
