I don't understand the first one
The first is more or less easy to understand if you know the value of the secret Nonce K using in an ECDSA signature you can calculate the private key with no effort.. Now some of you maybe heard about That a repeated R value in two signatures of the same public key can lead to disclose the Private Key... well that is the same if you KNOW the relationship between two signatures if you that K1 is X value +/- K2 or some other weird relationship them the Private Key can be solved easily.
About that i did a real puzzle in:
Second small puzzle about ECDSA and other computers topicsHere is satoshi response to a hash 256 getting broken in future
Thank you for the satoshi quote about it.
Do you imagine that? if Sha256 is broken, the entire bitcoin mining industry will be collapsed by a single machine with a proper algorithm... And not only that most of the security of internet that depends of sha256 will be compromised in someway.