Switching files from one hard drive to another

Hi,
I have to say that I am very pleased with Digital Storm's customer service and I've had my computer now for about 2 years. 
With that said-I have a problem because I don't know how to get my Oblivion and Sims 2 information from one hard drive to the other without messing everything up.

I have the one hard drive the computer came with but I've downloaded so much stuff that I had to get a second hard drive, an external one, to transfer all of these downloads into.

I have the second hard drive connected. I've backed up my computer files onto it as a back up and then I copied and pasted my Oblivion folder and EA Games folder into the second hard drive. 

I haven't taken the Sims 2 or Oblivion folder out of my original hard drive. I'm scared if I do, I'll lose everything.
I copied and pasted the whole "EA Games-Sims2 and all of the expansion packs from the Progam files as well as the ones under EA Games from my Documents file and then I just copied and pasted the whole Oblivion file from the Games folder.

Did I copy and pasted the right things, the right way? Is there anything you know of that I missed or shouldn't transfer over?
Please help me with this. I really don't want to lose the many many hours I've spent downloading all of this stuff. Thanks!

Oh, I guess I should have put this in the hardware section.
One other thing.  Can I unplug my external hard drive to replug it into another place without messing up everything? I tried to safely remove the hardware but it keeps telling me to come back another time because it cannot be stopped right now. Do I have to first shut down my computer to unplug it? 


Edited by Pineapplerum - 23 Jan 2010 at 2:24pm