Are sins forgiven by carrying out the حد (prescribed punishment) or through expiations, and is love permissible between two unmarried individuals provided they adhere to Islamic law?

The prescribed Islamic punishments (Hudud) atone for sins, as do the legally stipulated expiations (kaffarat), such as the expiation for an oath or for Dhihar (a pre-Islamic form of divorce by which a husband would declare his wife to be like his mother's back). These expiations atone for the sin and remove its effect. As for a man's love for a non-mahram woman (a woman he is not permitted to marry), if it is involuntary, he is not held accountable for it. However, if it stems from an unlawful cause, the servant is held accountable for it.