We are allowed to and encouraged to pray for everyone.
In the Divine Liturgy we pray "for peace in the world," and "Remember, Lord, the city in which we live, every city and country, and the faithful who dwell in them. Remember, Lord, the travelers, the sick, the suffering, and the captives, granting them protection and salvation. Remember, Lord, those who do charitable work, who serve in Your holy churches, and who care for the poor. And send Your mercy upon us all." In addition to this we pray "For our country, the president, and all those in public service, let us pray to the Lord."
We pray for the salvation of all, and for the well being of all.
I read in "The Mountain of Silence" by Kyriacos Markides that Elder Paisios of the Holy Mountain is said to have even prayed for the salvation of the demons.
So yes, pray for everyone.