How can a person who has committed great sins — including deceiving and insulting girls, addiction to pornographic websites, and abandoning prayers — repent and be absolved of his wrongdoings? And do jihad for the sake of Allah or honoring one's parents expiate his sins?

Your awareness of your mistake and the gravity of your actions is a correct start, for a believer fears his sins. You must initiate sincere repentance that fulfills its conditions. If you weaken and return to sin, repent again and do not despair of Allah's mercy, for He, glorified be He, said: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'" Repentance is accepted even if the sin is repeated, as long as it is with the intention of abandoning it, remorse, and a firm resolve not to return to it. You are not unjust to the girl who complied with you in the relationship. As for the one you wronged by slandering, you must seek her forgiveness unless you fear a greater harm, in which case you should make abundant supplications for her. Losing prayers from their prescribed times is a grave neglect, so repentance is due, and you must make up for what you missed by your best estimate. Be diligent in seeking what helps you remain steadfast and keeps you away from the evil of human and jinn devils.