The network uses pki, but what exactly is being encrypted. What is to stop someone else from sending a message to the network stating that he is you and he transacts x funds to y account, im sure this is where the encryption comes into the equation but how.
If you have someones public key, you can quickly check if the message was signed with his private key or not. So the nodes would simply reject transactions that were not signed with the proper private key.
I'm not sure about the details, since addresses are not actual public keys, but hashes of those keys, but I'm sure someone else will fill in the details.
Also i understand what the theory behind the usefulness of proof of work systems, such as forcing a server to solve a problem before being willing to receive a message from it in order to prove that their is a cost involved for the sender limiting the potential profitability of spam, but i cant for the life of me figure out how it factors into the whole bitcoin equation. If im asked to solve a complex problem then rewarded for solving it, whos asking the question, what method is used to generate the problem.
You are trying to find 256 bit hashes with certain number of zeros at the start of the hash. All the nodes together agree on the difficulty, so that the average number of hash hits is one every 10 minutes.
Every hit puts a new block at the end of the chain, and the chain grows. The deeper your transaction is in the chain, the harder it is to change it, since it takes a lot of processing power to generate each block.
Also isnt it possible that two different public keys could return the same hash value, i know its unlikely but if people are using this service 100 years from now on a global scale there could be a LOT of transactions by then.
Very very unlikely. Somebody needs to calculate, if you generated new key pair million times every second, now much time you need to have 50% chance of hitting it. My guess is that the age of the universe would still not even scratch the surface.
And even if it happens, I guess two people would be able to send the same coins to somebody else, but still only once.