How does the protocol prevent miners from building off of a fraudulent blockchain? Let's say someone creates a fraudulent block and finds a nonce that solves the hash puzzle. This block is broadcasted, its hash easily verified, and it's added to the blockchain. What prevents a miner from hearing this block and adding it to its blockchain such that it uses the hash of this fraudulent block as the previous hash field in the new block it is trying to solve? Couldn't this then create the longest blockchain at a fork and thus become accepted? 

When do mining nodes give up on a certain block? Once a block with the correct nonce is found for a given previous block, don't all other nodes mining a block with the same previous node have to start over?
A miner could create a block with an incorrect transaction, but this wouldn't be accepted by the honest nodes in the network. The honest nodes would attempt to validate the transaction, fail and then not propagate the block to other nodes.