How are malicious nodes prevented from, after getting the nonce of a new block found by someone else, broadcast it to the other nodes claiming it to be its?
Also, how does the bitcoin system solve the situation of an evil miner who has found the nonce of a block and then sends it with 2 different nodes, each one reaching 50% of the network, therefore having a problem of ownership of this work?
Finally, if all nodes have to check a broadcasted nonce to prove it's legit, how does the network defend against attacks in which thousands of ip adresses (e.g. botnet) start sending wrong nonces, causing a cpu DDoS because of all the peers hashing and checking these nonces.
Thanks for the answers.
Note: As the three questions are related I thought that putting them all in a single question was correct, if not told me and I will edit the text to only contain the first question, placing the other two in different questions.