1 - No problem if the HDD has finished it's job (that is usually 1-2 seconds after the OS reports the file transfer is finished)
2 - Again if the HDD is not writing or modifying anything there is no loss (except the one in the main RAM)
3 - No problem at all. But the less it moves, the better.
4 - Same as 1 and 2
Both hardware and software are designed not to avoid, but to limit problems like those. Eg the OS usually prefers to disable the HDD write back cache by default (less performance) just in order to limit the data loss probability in case of a power failure. Personally I loved it the way it was with AT and MS-DOS. You just pressed the off button and it was turning off without ifs and buts. And it was your responsibility to make sure floppies and HDDs had finished their job. But it was too easy at the time. You always knew what was running in your PC and when. Right now there are so many background staff silently going on that it drives me nuts.
BTW, using an external HDD, the main thing I'd be worried about is overheating. Not only does it have no fan, but it is inside a tight case as well.