A private key is a cryptographic tool that verifies you are the owner of the app. Any build that is being updated to the Google Play store must be signed by your private key to prove it is a legitimate build.
So each different application that you want to upload to the store should have its own private key. If you ever lose this key, you will not be able to upload any new versions of your app, so make sure to store it somewhere safe and make backups!
However, you can store multiple private keys in the same keystore for convenience. (Although I do not, I find it more convenient to have a different keystore for every project as well.)
An alias is simply an easy to read name for the key. Nothing more or less.
It's worth noting, when you do an Eclipse "Run", it uses something called the debug key to run the application. This works fine because you are not trying to upload this build to the store, but this is why you need to use a separate build process to build your application for deployment.
The lifetime validity is a technical requirement. Just set it way in the future and don't worry about it.