Oh? I didn't know you could drag new icons on, but I often do add or delete icons from it. I had to take off the mail app because I never use it and I would open it on accident and my computer would freak out because it's not set up or anything.
I know on my computer, it also shows a black dot underneath the apps that are in use in the dock. You can also place your dock on the side of the screen instead of across the bottom. Should default at the bottom though. It drove me nuts that the macs at school had the dock on the side instead of bottom.