Replacing the harddrive cover with a plastic see thru cover is a common case mod project. It's only done with older drives though, since even taking the most care, the success rate is still hit or miss. Running it free air, even just as display is not going to work, like mentioned. platters with head crashes do not look all that good.
If you google search, you should be able to see these projects, most use a plastic bag to protect the hardrive from dust while doing the procedure. You have to watch out what glues or sealants you use as well, because some outgas particles that will crash the heads as well.
As for driving the hdd, yes, you'll need to get an IDE connection made up with a microcontroller. There maybe another way to drive the motor and head directly, but I'm not certain that's very easy.
EDIT: Someone posted a HDD clock project earlier, but there was no head, just the spinning platter.