Mass stipends to priest for offering Mass for a particular intention is regulated by Canon Law 945-958:
Can. 945 ß1 In accordance with the approved custom of the Church, any priest who celebrates or concelebrates a Mass may accept an offering to apply the Mass for a specific intention.
ß2 It is earnestly recommended to priests that, even if they do not receive an offering, they celebrate Mass for the intentions of Christ's faithful, especially of those in need.
Can. 946 The faithful who make an offering so that Mass can be celebrated for their intention, contribute to the good of the Church, and by that offering they share in the Church's concern for the support of its ministers and its activities.
Can. 947 Even the semblance of trafficking or trading is to be entirely excluded from Mass offerings.
Can. 948 Separate Masses must be applied for the intentions of those for whom an individual offering, even if small, has been made and accepted.
Can. 949 One who is obliged to celebrate and apply Mass for the intentions of those who made an offering, is bound by this obligation even if the offering received is lost through no fault of his.
Can. 950 If a sum of money is offered for the application of Masses, but with no indication of the number of Masses to be celebrated, their number is to be calculated on the basis of the offering prescribed in the place where the donor resides, unless the donor's intention must lawfully be presumed to have been otherwise.
Can. 951 ß1 A priest who celebrates a number of Masses on the same day may apply each Mass for the intention for which an offering was made, subject however to the rule that, apart from Christmas Day, he may retain for himself the offering for only one Mass; the others he is to transmit to purposes prescribed by the Ordinary, while allowing for some compensation on the ground of an extrinsic title.
ß2 A priest who on the same day concelebrates a second Mass may not under any title accept an offering for that Mass.
Can. 952 ß1 The provincial council or the provincial Bishops' meeting is to determine by decree, for the whole of the province, what offering is to be made for the celebration and application of Mass. Nonetheless, it is permitted to accept, for the application of a Mass, an offering voluntarily made, which is greater, or even less, than that which has been determined.
ß2 Where there is no such decree, the custom existing in the diocese is to be observed.
ß3 Members of religious institutes of all kinds must abide by the decree or the local custom mentioned in ß1 and 2.
Can. 953 No one may accept more offerings for Masses to be celebrated by himself than he can discharge within a year.
Can. 954 If in certain churches or oratories more Masses are requested than can be celebrated there, these may be celebrated elsewhere, unless the donors have expressly stipulated otherwise.
Can. 955 ß1 One who intends to transfer to others the celebration of Masses to be applied, is to transfer them as soon as possible to priests of his own choice, provided he is certain that they are of proven integrity. He must transfer the entire offering received, unless it is quite certain that an amount in excess of the diocesan offering was given as a personal gift. Moreover, it is his obligation to see to the celebration of the Masses until such time as he has received evidence that the obligation has been undertaken and the offering received.
ß2 Unless it is established otherwise, the time within which Masses are to be celebrated begins from the day the priest who is to celebrate them receives them.
ß3 Those who transfer to others Masses to be celebrated are without delay to record in a book both the Masses which they have accepted and those which they have passed on, noting also the offerings for these Masses.
ß4 Each priest must accurately record the Masses which he has accepted to celebrate and those which he has in fact celebrated.
Can. 956 Each and every administrator of pious causes and those, whether clerics or lay persons, who are in any way obliged to provide for the celebration of Masses, are to transfer to their Ordinaries, in a manner to be determined by the latter, such Mass obligations as have not been discharged within a year.
Can. 957 The duty and the right to see that Mass obligations are fulfilled belongs, in the case of churches of the secular clergy, to the local Ordinary; in the case of churches of religious institutes or societies of apostolic life, to their Superiors.
Can. 958 ß1 The parish priest, as well as the rector of a church or other pious place in which Mass offerings are usually received, is to have a special book in which he is accurately to record the number, the intention and the offering of the Masses to be celebrated, and the fact of their celebration.
ß2 The Ordinary is obliged to inspect these books each year, either personally or through others.
The amount of a stipend, per Mass, is usually determined by the Province. Most dioceses in the United States, have set the Mass Stipends to $5 - $10 dollars. The purpose of the stipend is to help support for the needs of the priest. If a stipend is more than the set amount the priest may keep only the amount determined by the Province or diocese with the rest given to the parish. If a person cannot afford a stipend he may still ask for a Mass Intention.
As for offering a Mass for God the Father, this is inappropriate. God does not need a Mass said for Him. He is the Mass. Every Mass is in "honor" of our Lord God.
Mass intentions may be for those deceased, those alive, or to thank God for something.
In spiritual warfare it is a certain benefit to have Masses said, and intentions offered in the Divine Office, for the afflicted person.
As for "tradition-leaning" groups, all groups that are loyal and obedient to the Pope and the Magisterium in union with him are "tradition-leaning" groups. Associations such as the SSPX are actually anti-tradition because they fail on the very first tradition: obedience.
But, I understand what you are asking. You can do a google search on FSSP and find associations and parishes of the FSSP.