Welcome to Techsurvivors Anne!
If you are referring to icons on your desktop - they're simply aliases to the programs themselves - so if you delete them, the icons will be gone, but the programs will still be in your applications folder. If you want to delete the programs too, then you need to drag them to the trash, along with all their extensions etc. Use Sherlock to find all the bits, by searching on the name of the program.
I'm assuming that you're using OS 9? You certainly don't have to, and probably shouldn't, delete the Energy Saver Control Panel (if you mean actually putting it in the trash and throwing it away) in order to get the Mac to do what you want it to do. Instead, you should go into the control panel and set all the energy controls, like turning off the monitor, to "never".
I'm not quite sure what has happened if you've truly tossed the panel. Could be that the iBook has some default setting or other that it uses. Are you sure the control panel isn't in your disabled control panels folder?
If you send me your email address, I'll send you a new Energy Saver Control Panel so you can reinstall it and correct the settings to something you want.
Your photos are absolutely lovely by the way!!!