What is the point of installing a game?

Much like those in your computer, optical drives spin at varying speeds based on the data they're trying to read. It doesn't mean much, and in general should happen more on startup and loading screens. If it gets to be too loud or disruptive, you always have the option to install games to your hard drive. Note you'll still need the disc in the drive, but it will attempt to read data from the hard drive instead of the disc, making it generally faster and quieter.

I generally keep the game that I've been playing the most installed on my xbox and uninstall games I haven't played in a while to keep space free. I appreciate the faster load times and quieter operation, but it is by no means required that you install games to your hard drive.

This will allow you to install the game directly to a hard drive (if you bought one), or to an external USB device. This will load the game from that device, rather than from the DVD. It'll definitely cut down on any noise from reading the disc, and typically (but not always) results in faster loads for games. You do have to have the game disc in the drive when loading it up and playing though for security reasons.

I'm not too sure about the first part of your question but I can certainly answer the second part. You can indeed play games without installing it, if you don't install the game the game will simply run off the CD. If you do decide to install the game you will still need the CD to play the game (prevents users installing the game and then returning the game).

Installing the game has advantages: - Reduces game load times - Apparently helps prevent the "red ring of death"