Can You Tell Me Some Useful Character Building Exercises As An Actor?

No.  And the reason that I say no is that there aren't any useful character building exercises for an actor.  The character was already built by the playwright in their construction of the play.  Your job, your lookout is not to build a character, but to tell the story of the play.  

The only character that needs to be built is your own, and I don't mean a fictional character.  Your character.  The stronger and more achieved your character is, the better.  Your character is the most important character in the theatre. As Stanislavski once said (I paraphrase a little here 'you are a thousand times more interesting than any character in a play'.

Exercises such a writing out biographies for your character have the appearance of utility, but they are essentially just talisman's to ward off the evil bad performance demons.  The theatre is full of such mythical baloney.