Are there special merits for burial in Al-Baqi‘, and will everyone buried there be among the people of Paradise, and are the dead punished in their graves there, and is it permissible to print and distribute translations of the Qur’an on behalf of the deceased, and what is the appropriate supplication for the deceased in Al-Baqi‘ from a distance?

There is no Hadith indicating the virtue of burial in Al-Baqi'. Rather, there is an encouragement to die in Medina for one who endures its hardships, so that the Prophet, peace and blessings be upon him, may intercede for him. The death of the father after performing 'Umrah and its rituals is a sign of good. It is not necessary to visit the grave to benefit the father; supplicating for him anywhere will benefit him, just as giving charity on his behalf will benefit him.