You can install the HDD into anther machine with an active operating system and boot drive to access any personal files and transfer them. You cannot install the drive into another machine as the primary drive and boot into windows 8. The hardware is different.
Actually you can. On first boot up, Windows will detect hardware has changed and go through the set up process to install generic drivers unless it already has vendor specific drivers in its repo. The first time you boot it up will take the longest for this so don't be surprised or think the process has frozen when this happens. The worst thing you can do is reboot it during this phase which can corrupt your drive.
For the most part it will work. There is maybe a 5-10% chance it can blue screen but you shouldn't run into that issue unless you use very obscure hardware. Though this method is never recommended, it's not the end of the world if you do it either. It's always good to start fresh anyway.
You will need to reactivate your copy of Windows as it will have detected the massive hardware change. And there is a chance that you won't be able to re-use the key as Microsoft will see it as a new computer.