Is it permissible to prepare a weekly feast for the married couples from the village and their relatives after Friday prayers, and is it permissible to invite people to it in the mosque?

There is no legal impediment to providing and distributing food in the mosque; rather, it may be among the good deeds encouraged by Islam, especially if the poor and needy are present. The Prophet, peace and blessings be upon him, encouraged feeding people, and children used to rejoice on Friday because of the presence of food in the mosque.