If someone has lost one of his parents, can you perform Hajj for him/her? If yes how? Will Allah forgive you if have wronged one of your parents if you had not asked forgiveness from them before they die but you ask from Him? What are the different ways of paying Zakah for the dead?

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 is His slave and Messenger.

If one of the parents was able to perform his/her obligatory Hajj but did not perform it and died leaving enough property that is sufficient to perform Hajj on their behalf, then in this case, it is compulsory for their children or inheritors to perform Hajj for this parent themselves, or to appoint someone else to perform Hajj on his/her behalf. The expenditure of this Hajj is deducted from the inheritance left by the dead person.

The evidence for the above ruling is the Hadeeth of Ibn ‘Abbas that the Prophet said: “Fulfill the right of Allah for Allah's right is most deserving to be fulfilled.” [Al-Bukhari]

If the dead parents do not leave what is sufficient for the expenditure of Hajj, then the children are not held responsible to perform Hajj on their behalf. However, it is permissible for them to do so as an act of being kind to one's parents.

Some scholars are of the opinion that performing Hajj on behalf of dead parents is not compulsory unless they left a will specifying it to be done, in which case, it should be carried out only from the one third of the inheritance not exceeding it.
The person who wants to perform Hajj on behalf of a dead person or the one who is physically not capable to perform his Hajj, should have already performed his own obligatory Hajj. Ibn ‘Abbas narrated that the Prophet heard a man saying: ‘Labbayk on behalf of Shubrumah.’ He asked: ‘Who is Shubrumah’? He replied: ‘A brother or relative of mine’. He asked: ‘Have you performed Hajj on your own behalf?’ He said: ‘No.’ Then, he said to him: ‘Perform Hajj on your own behalf, then perform it on behalf of Shubrumah.” [Abu Daawood and Ibn Maajah]

So, one of the children or someone else who has already performed his Hajj could perform the Hajj on behalf of the dead person as described in the Sharee’ah. Therefore, he should start the substitute Hajj from the country where the person was living if the money is sufficient for Hajj; otherwise, from the nearest country to him. The substitute person may perform any of the three types of Hajj; i.e., Hajj Al-Ifraad, Hajj Tamattu', or Hajj al-Qiraan as long as there is no will defining the kind of Hajj to be performed. If there is any such will, then one should act according to it.

Treating one's parents unjustly is among the greatest sins. Allah has forbidden injustice to oneself and to other people as well. A Muslim is not allowed to do wrong to anyone, then how could it be imagined that he can behave unjustly towards his own parents. Allah has ordained on Muslims to be kind with their parents, and to be obedient to them. Abu Tharr narrated that the Prophet said: “Allah, The Exalted and Glorious, said: ‘My Servants, I have made injustice unlawful for Me and unlawful for you, so do not commit injustice against one another.” [Muslim]

Not being obedient to one's parents and neglecting their orders is considered as an impious act. So, undoubtedly being unjust to them is strictly forbidden and leads to severe punishment. The Prophet said thrice, “Should I inform you of the greatest of the great sins?” They said, “Yes, O Allah's Messenger!” He said, “To join others in worship with Allah and to be undutiful to one's parents.”

The Prophet joined being undutiful to one's parents with Shirk (polytheism). This evidence alone is sufficient for every Muslim to abstain from being unjust to his parents.

If the father died before this son asked him forgiveness, then the latter should make sincere repentance, ask Allah to forgive his father, give charity on his behalf, and keep good ties with his father's blood relatives.

If one acts according to what is mentioned, then we hope that Allah will forgive him and cover him with His Mercy. Allah Says (what means): {But indeed, I am the Perpetual Forgiver of whoever repents and believes and does righteousness and then continues in guidance.} [Quran 20: 82]

The Zakaah of a dead person should be paid from his money before distributing his property among the inheritors according to the preponderant opinion of Muslim scholars.

The Prophet said: “Fulfill the right of Allah, for Allah's right is most deserving to be fulfilled.” [Al-Bukhari]

A few scholars are of the opinion that Zakaah should not be paid except if the dead person leaves a will to do so.
The first opinion is the correct one, as we mentioned earlier.

Allah knows best.