No. During the mining process, the miner assembles a set of transactions and other data to be put into the block header. Using SHA256, the block header is hashed twice and if and only if the hash meets the target, the miner will broadcast the block to the network.
The miner will not broadcast the block if there is a block there has been broadcasted before his at the same height. If he does, every node in the network will simply reject it as there is a chain with a longer proof of work. The miner can only be rewarded if his block is valid and is recognised as such by the network. There is simply no reason for anyone to broadcast a block that is below the current block height if they won't get rewarded for it.
The miner looses against miners, the block becomes orphan, and the miner's chain reverts back to the main chain (somehow) and he waits for the next block to be mined.
No. While the miners are technically competing against each other, they are still somewhat working together to build the chain. If the miner has less than majority of the hashrate, it is not profitable for him to have a competing chain to the rest of the network since he will lose with the others holding more hashrate than him and thus possibly having a longer chain.