By tying takhi to karan instead of gautam, it is a symbolic hint that karan will go any extreme to protect his sister. So he took the blame.
But why shoba is quite all thse time. Because karan ne kasam le liya. But anyway she wqill confess the crime and go to jail for 20 years and come back after leap. Because ekta does not want her to marry for the third time. So just send her to jail.