Luna Manager is one of the handiest apps for homebrewers allowing you to control multiple aspects of Luna with a simple GUI
Luna Manager requires the package manager service (that preware uses) to be installed to work.
Rescan Option allows you to rescan your launcher. So when you install a new app and icon doesn't show up this will generally fix that.
Restarting Luna is a good solution when you install patches, themes and some advanced homebrew apps to apply the changes without the need of a full reboot of the phone. It is a lot faster then an entire reboot and comes in quite handy. Keep in mind that it will close all your currently open applications.
Restarting Java is used for advanced home brew applications and installations for new services to take effect. Much easier then an entire reboot of the phone. Keep in mind This will cause your phone to lose network connection and be pretty sluggish until it is done restarting.