After exiting the applications on my Galaxy nexus, they appear on the recent applications list. Do they still use CPU/battery? Do I have to remove them from recent applications list in order to save battery?
The recent applications list show only what applications have been recently used, it doesn't check whether they're still running or using memory/CPU. Therefore, this list doesn't affect battery use one way or the other.
Instead, you might want to check
Settings -> Apps -> [swipe to the right] to show running applications, processes and services. Here you can see the apps that are using your device and consuming battery, and kill unnecessary processes by tapping the app and then