1 ) Any blockchain downloader client available, will show continuous logging when downloading the blockchain with block numbers and all, so you can use that to determine whether it is downloading correctly or not. the client will redownload corrupted blocks and ensure their integrity.
2) If you are trying to download the ethereum blockchain right now, you are going to download all the blockchain ( a new idea is being debated on whether that should stay or not) so yes it contains the blockchain data.
3) The blockchain download will be complete when the terminal (client ) you are using, displays the last block number that has been mined, you can check that out on many websites.
4) as long as you are running the terminal who you started downloading the blockchain with, it will keep synchronizing. you can shut it down and rerun the client again to go through the process of downloading new blocks.