From what you've written earlier, you want to clone your old drive to your new drive. Thus use the clone option in Macrium, and triple check that it is setup to clone the correct drive to the correct desination drive. (Your 1tb old to the 3tb new). If it doesn't let you resize the partition form 1tb to 3tb, you can do that later in windows. Off the top of my head, use the "clone this disk" option under the drive you want to clone (should have a check mark by it too). That should pop up a screen to select the destination drive.
An image is a big file you make that can later be used to restore the drive/partitions etc. on one or more drives. It is what you use for long term backups. A clone is where you make an exact copy direct from the source drive to the new empty drive. An image can be used instead of a clone but it will likely take longer as you make the image file "backup" and then restore the image to a new drive. And don't bother with a full format unless you're paranoid about the new drive being bad or are putting these disks into a real server/NAS box etc..
"Would "xcopy e:\ f:\ /e /h /k" copy all the files from e: to f:?"
Eh, try
http://www.codesector.com/teracopy then