Assalaamu alaykum wa rahmatullaahi wa barakaatuhu. Shaykh, my question is with regards to revenge/forgiveness. If I was wronged, verbally or physically, in any way and choose to forgive the person and ask Allah, the Exalted, to simply restore my rights to me and (and not ask Allah, the Exalted, to take revenge on my abuser due to my inability to), if I forgive them, does that mean that they will be absolved of blame for their abuse on the day of judgment? So, if I forgive them and they do not repent to Allah, the Exalted, and/or continue abusing me even though I forgive them, will they still be held accountable and be punished for it on the Day of Judgment even though I forgave them seeking Allah's pleasure? May Allah reward you. Wassalaam.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

First of all, we note that your question has some contradiction and is quite ambiguous. We shall answer the question in the following points according to what we understood from it:

1) If you supplicate against the one who wronged you, you have retaliated against him and have missed the reward of pardoning. Al-Munaawi said:

"The Prophet, sallallahu ‘alayhi wa sallam, said, 'Whoever supplicates against the one who wronged him has triumphed over him (i.e. restored his right).' This means that if the wronged person insults the honor of the one who has wronged him, it decreases the sin of the one who wronged him and decreases the reward of the wronged person proportionally. This clearly indicates that when the wronged person retaliates, even if only verbally, he has taken his right from the one who has wronged him, so he neither bears sin nor deserves reward. The hadeeth hints that it is disliked to seek revenge and that it is recommended to pardon and expect the reward from Allah instead. Allah, the Exalted, says (what means): {And whoever is patient and forgives - indeed, that is of the matters (requiring) determination.} [Quran 42:43]..." [Faydh Al-Qadeer]

2) You asked, "If I forgive them in the worldly life, will they still be held accountable and be punished for it on the Day of Judgment?" You should know that committing injustice against people involves the violation of the rights of Allah and the rights of the wronged people. When the wronged person forgives the one who wrongs him, he is giving up his right, but this does not apply to the right of Allah. The wrongdoer must repent to Allah to clear his liability from neglecting the right of Allah. If he does not repent of his injustice, he is subject to the relevant warning even if the wronged person forgave him, unless Allah, the Exalted, pardons him.

Al-ʻAyni said:

"Regarding the command to 'seek his forgiveness' (in the hadeeth: Whoever has wronged his brother with regard to his honor or anything else, let him seek his forgiveness today...), Al-Khattaabi commented on it, saying, 'This means that he asks the wronged person to forgive him and clear his liability, because this person's liability with regards to prohibited backbiting cannot be cleared except by the forgiveness of the backbitten person. A man once came to Ibn Seereen and said, 'Please acquit me, for I have backbitten you?' Ibn Seereen replied, 'I do not deem lawful what Allah has deemed unlawful, but regarding what is relevant to me (of your sin), then I acquit you of it." [ʻUmdat Al-Qaari]

3) It is permissible for you to forgive the mentioned person for wronging you in the past and in the future. Ibn Al-ʻArabi said, "A loan may be material (lending someone money) or non-material (pardoning others' offenses against his honor). The Prophet, sallallahu ‘alayhi wa sallam, said, 'Can anyone of you not be like Abu Dhamdham?' The Companions asked, 'Who is Abu Dhamdham, O Messenger of Allah?' He replied, 'When he gets up in the morning, he says, ‘O Allah, I offer my honor as charity to your slaves?’ (i.e. I forgive those who backbite me, insult me, or tarnish my honor).'" [Mash-hoor Al-Aathaar]..." [Ahkaam Al-Quran]

Ibn ʻUmar, may Allah be pleased with him, said, "Give those who wrong you loans from your honor (i.e. pardon the offenses of others against your honor) for the day you might be in dire need; if someone insults you, do not retaliate or request subjecting him to the prescribed punishment so that you would earn greater rewards on the Day of Judgment."

Allah knows best.