When you are finished using an application, you can either "back out" of it to the home screen using the back arrow key, or you can click the menu button and select "exit," in most apps.
Leaving apps open while going from one app to another, or when you powering down your device, uses up a lot of resources needlessly.
There are apps available in Market which address the lock screen preferences, just do a search in Market under "lock screen," etc.