Is it safe to remove the "Install Xcode" application after installation? Is it safe to remove the Xcode 4 installation program from my Applications folder after I installed Xcode? If there is a free update, will I still get it, or do I have to buy it again?

The installer is 4,58 GB, which is space I could use on my hard drive!
Yes, it’s safe to remove the XCode installer, once you’ve installed the XCode tools. XCode tools can be downloaded for free from Apple’s website. If you are registered at developer.apple.com, you may also download the iPhone/iPad SDK from developer.apple.com, to be able to create iPhone/iPad software (the XCode tools that ship with MacOS X will only allow you to build applications for Mac OS).