What does this strange asterisk for text style mean?
The asterisk simply indicates that the default style has been changed. For example, if you have a piece of text styled as “body”, and then change the font, you will see an asterisk appear after the style name to let you know it is no longer the original body style.
If the change that you have made to the styling will be used throughout the website, then I would suggest to click the down arrow. The next thing to do would be to press the + icon at the top of the window. This will create a new style and allow you to rename it etc.