Can you reinstall World of Warcraft after you uninstall it

Yes, that is possible. If you want to reinstall it from scratch, you can do it from the original CD or download you had, or you can log in to your battle.net account, click on your World of Warcraft game and choose "install client". You will then download and install the game and all expansions linked to your account.

You can also copy the installation from another PC (using CD, USB stick or external hard drive) and run WoW after it has been copied to your PC.