This is Chinglish. You can also say, "I will be free (for) this Saturday" besides the other answers. It implies that you are free the entire day unless qualified like, "I will be free this Saturday except...."

It doesn't sound very natural. It's better to say: I will be free all day Saturday. or I will be free the whole weekend.

Your answer is ''correct but not common," grammatically correct but not the way we commonly express that thought. I usually say, "I'll be free all day Saturday."

I would say: "I am free the whole day on Saturday." or "I would be free on Saturday."