Can I install Oracle 11g on a hard drive. Can I use this hard drive in another computer where 11 g is not installed and just play a bit with Oracle?
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That's not possible. Oracle install creates several services, modifies the registry to include
And if you have configured the data & log files to be on separate drives, then that's another whole different ballgame.
If you need to play with something, just use a Virtual Machine. Oracle provides several VM appliances and that you can just download & start playing with. If you need your live data to work with, export the data, import it into the VM & play to your hearts' content.