Okay so I understand more now, a complete brute force would take multiple billion years because of the magnitude of possibilities (2²⁵⁶) Than you to https://bitcoin.stackexchange.com/questions/2847/how-long-would-it-take-a-large-computer-to-crack-a-private-key
But I'm still getting my head around the verification process for checking signatures. Even using the public key to cut down the possibilities there would still be billions of years of computing to crack the key. I was under the impression that you could get more info about the private key from every signature you see but that's incorrect, isn't it?
Also, what would happen if someone were to just send out random falsified transactions? Wouldn't that slow down the other nodes? couldn't you just write all the false transactions and have other nodes verify them?