"Install Xcode" in Applications, necessary after I've installed Xcode?

Do I need the Install Xcode after Xcode is installed?

Do you know of any reason it installed an installer to Applications?

You may want to keep it in order to be able to download delta updates instead of the full version when updating via the Mac App Store.

If you don't care about that or care more about disk space, you can delete it (you'll be asked for the administrator password) and continue to use Xcode.

It's not necessary to keep the XCode installer file after XCode is installed. However, you may wish to consider keeping it stored somewhere as the XCode download is relatively large.

It's probably in the Applications folder because this is where the App Store puts downloaded packages by default.

The Mac App Store is setup to install in /Applications, but some applications, like Xcode, are way more complicated to be contained in an .app file.

So they need to use an installer, which is going to add the /Developer folder which itself contains multiple applications (Xcode, Dashcode, the iOS simulator, etc.).