No, you are not doing it wrong.
By clicking the star you are marking it as a favourite, which as you pointed out pops them in to the Favorites tab in your profile making it easy for you to find them.
You will receive notifications of any edits, new answers, comments & edits to answers.
Marking questions as favourites does not affect the reputation of ...
Click the Star under the vote count for any question to mark it as a Favorite.
See also: How do favorite questions work?
Alternatively, every question has an RSS feed. The link is in the lower right corner after any answers. Just add that to your favorite feed-reader.