Q. For whom is Mass for?
A. If you listen closely to the prayers at Mass, you will notice that at one point or another we pray for everyone. This means that the benefits of each Mass extend outward in space and time from the community gathered around the altar to all the world and its people. This is most clear in the four Eucharistic Prayers, and it is implied in the other prayers.
All the prayers of the Mass are raised to the Father for the entire people of God. The priest acts both in persona Christi (in the person of Christ, i.e. by the grace of his ordination re-presenting Christ) and also as the representative of the people of God to the Father. When he prays, it is as if he is 'gathering up' the prayers of the people who are present, as well as the prayers of those who are not present physically. For example, in the Opening Prayer, the priest prays that God may bestow some blessing upon his people. In the Mass for the Baptism of the Lord, the priest prays: 'May all who share in the sonship of Christ follow in his path of service' or 'Keep us, your children born of water and the Spirit faithful to our calling.' This prayer is not limited to himself, or to those who are in the building when it is prayed. It is a prayer for all the people of God.
In each Eucharistic prayer, we pray specifically for the whole Church, for the pope and the diocesan bishop, for all the living and all the dead. This is especially clear in the third and fourth Eucharistic Prayers.
In the third Eucharistic Prayer we pray that the sacrifice of the Mass 'advance the peace and salvation of all the world,' for 'your children wherever they may be,' and the dead, including 'all who have left this world in your friendship.' In the fourth Eucharistic Prayer we pray 'all your people, and all who seek you with a sincere heart,' and for the dead 'whose faith is known to you alone.'
Of course, the General Intercessions usually have the format of praying for the Church, the nation, those who are in difficulty, and the dead.
Therefore, the Mass is for everyone - everyone may attend and pray with us (though not everyone may receive Holy Communion), and the prayers are said for everyone, but most especially the members of the Church on earth and in purgatory.
The priest certainly includes in his Mass prayers all who have asked him to pray for them. However, as a means of supporting the clergy, the priest may accept one monetary gift (called a stipend), to remember a particular person or intention in his prayer. This is a pious way to help support the clergy; it is not a guarantee of extra blessings to the person. To prevent unseemly profiting from saying Mass, the priest may accept only one stipend per Mass, but that does not limit him from remembering others in his prayers. Indeed, the priest cannot limit his prayer to only one person, or one group of persons, because he is acting in persona Christi, and Christ presents all the baptized to His Father.