System crashes and freezes can indeed trash hard-drives - or at least the data on them. This is pretty rare tho. The HDDs themselves do not crash when the system crashes. The system crashes and the drives finish writing out their buffer contents (in some milliseconds) and then just sit there waiting for further instruction. When the system is rebooted and the HDDs get an init command they close the file and write the check. If the drive lost power under such conditions it goes through a verify process and closes the file and writes the check on next power up (depending). Some may have noticed that after a system crash especially one where the power turns off to the drive bus, the drive or drives spend quite a bit longer initializing and/or house cleaning - causing slower boots and busy HDD access lights for longer periods than otherwise usual (sometimes even taking 10 or 20min to calm down). The OS works in tandem with this information to place a recovered folder in the trash with whatever files might be in question (depending).
This is normal and part of the drive firmware and saves us A LOT of troubles with the file system and file integrity. For this reason you don't need to worry about ejecting drives or anything like that. Of course if you know before hand the system is going down - which is the case with many developers during debug cycles - then it's a good idea to close al files and if you can take the drives off the bus by ejecting them or un-mounting them first.
By default TimeMachine backs up your entire OS as well as the Recovery Partition with the exception of a few common cache and temp folders. From the defaults you can add or remove drives and folders from the exclusion list.
There's no easy way to determine if the files are corrupt without opening them. You can do that with some utilities which will check the data against the written check. DiskUtility's Verify will verify file allocation tables and some other stuff. The time a file level verification takes up depends on the speed of the drive, the number of files, and of course the application speed. For a full 3TB drive this can take hours and hours. There may be some utility that can just verify specific folders but I haven't paid enough attention to know what they are. Have a search.