Yes you could, you would just need to buy a memory stick and transfer it all from one hard drive to the other. Or if you have xbox live then you can just download all your profile/game data from xbox live. You just need to recover it on the xbox live menu when you turn the console on.
You probably could, but I'm not sure about the profile. You could probably transfer it to an external drive and download the content from the external drive to the 120GB hard drive.