Doubts about the dock

Hey, I am now using my first mac, with Lion pre-installed

So I noticed that when you have an application opened, a light appears below the app's icon in the dock, but I don't understand how in this moment there is a light below the icons of Safari, iTunes, and Finder, and none of them have open windows!

I am only using one space btw

Another thing, when I first opened google chrome, chrome's icon stayed at the dock even after closing it... I have to right click in the icon and select quit for the icon to go away.

You aren't closing the app, you're only closing the window. Don't click on the red dot to close applications, it's not designed that way. You can either right click on the icon in the dock and click close, click on the app name at the top and click close.. or my personal favorite.. hold down the command key, and hit q. This will quit the application

...and if Finder is not running, neither is your Mac.

Aaahhh well that's just interesting. Thanks!!

the red dot doesnt close the application just the current window. to exit the application continue as you are or use the menu bar should be under the name of the application or file.my personal fav is command+Q