Also, does Google charge a fee for using adwords? Have you made money using Google adwords?

No, you don’t need website for using Google Adwords you can use free blog from blogspot or wordpress. If you want to earn some cash with google check out

http://makemoney-with-google.blogspot.com/

It will teach you how to make 1k a week, Check it out, you will be making a full income online in no time