Apostate prophet seeks the fair judge; why did the prophet Muhammad punish people?

In answer to the video "Muhammad's Destruction of Idols"

The Prophet never punished out of mere retaliation for a personal slight or injury. All his punishments, of believers and unbelievers alike, were for crimes committed against the public weal or infringements of the promulgated law; and even here his life contains acts of clemency in which he put mercy above justice. In 4:140 it says

"And indeed He has revealed to you in the Book that when you hear Allah's communications disbelieved in and mocked at do not sit with them until they enter into some other discourse; surely then you would be like them; surely Allah will gather together the hypocrites and the unbelievers all in hell".

This is a Medinan verse in which the prophet isnt told to forcefully silence the critics, even those mockers of the religion. He is simply to gracefully turn away from them and leave them to their own shamefull talk. A similar verse was revealed in Mecca 6:68.
The Muslims entered Mecca but the keys to the Kaaba were with Uthman Bin Talha, a non-believer who locked the door of the holy sanctuary upon learning of the Muslims' entrance in Mecca. He hid, refusing to hand over the keys, until Ali found him and snatched the keys from him, openned the Kaaba and the Prophet entered, prayed in it, after which revelation came down

4:58"indeed, Allah commands you to render trusts to whom they are belong to..".

The prophet understood that the Shaybah family had to be returned their possession; he thus ordered Ali to return the key to Uthman Bin Talha and excuse themselves. Ali then went to Uthman and gave back the key and presented their apologies for the wrong he had done to him by forcibly taking the key. Uthman b. Talha was shocked, he could not believe Ali was giving back the key to him as instructed by the Prophet Muhammad, the conqueror of Mecca, who could have done as he wished with anyone and anything within the city. Ever since, the guardianship of the Kaaba remained with Bani Shaybah, which is bestowed upon the elders of the family until today.

The soldiers and men of Quraysh who once levelled armies seeking to exterminate the Muslims by all means, persecuted and starved the Prophet and his powerless followers in the early days of his Call, brutalised and killed Muslim prisonners, war criminals in every sense of the word, came to the Prophet submissively. They thought they would most certainly be slain, just as they would have executed the Muslims had their tirelessly repeated plans worked. They knew very well that within their own customs retaliation and hatred were the rule of the game within the fabrics of the society and its order. Hatred and hostilities were passed down from one generation to the next and unwillingness to perpetrate revenge was considered a defect.

While attributing the promised victory to Allah alone, the Messenger, in the manner of the great men of God who show magnanimity once they are at the climax of their power and glory, contented himself with uttering what a previous Prophet, noble as him had uttered in similar circumstances. The prophet Joseph before him told his brothers who came to him in submission, seeking forgiveness for their faults against him

12:92"There shall be no reproof against you this day; Allah may forgive you, and He is the most Merciful of the merciful".

The prophet continued

"Let every wealth (wrongfully seized), every blood (wrongfully shed), and every revenge to be exacted belonging to the days of jahiliyyah be trampled under my foot, except the guardianship of the Kaaba and the bearing of water at the time of the pilgrimage; they shall be returned to their people (the Quraysh)".

The noble prophet finally recited the Quran verse which constitutes the epitome of divine justice

49:13"We have created you of a male and a female, and made you tribes and families that you may know each other; surely the most honorable of you with Allah is the one among you most careful (of his duty); surely Allah is Knowing, Aware".

With these words, Muhammad was giving a general amnesty to all Quraysh and all the Meccans. To realize the degree of generosity from the Prophet, one must recall the life threatening hardships which these people imposed on him and now that they were completely subdued by him, instead of thinking of vengeance, or at the very least demanding apologies and reparations, which was certainly his due, he forgave them.

This way he was displaying his function of "rasul", the embodiement of God's mercy to mankind.