Don't ever delete stuff from your main iTunes library, just to delete them from the iPod. You can set up iTunes to sync separately and differently to each device.
The latest iTunes may hide the sidebar. To show it, from the menu bar, under View, select Show Sidebar. The sidebar shows the iPod, under DEVICES.
How you remove songs from the iPod depends on how you have been loading songs, manually (by dragging songs to iPod) or by automatic syncing (by setting up the iPod's Music tab). If you need more information, please post back with the method you are using to load the iPod.
For reference, here is a general document about syncing to iPod