Why are these icons depicted on the fingertips? Is this a common image in Mexican Christian art?
Yes, this is a common motif! The hand symbolizes the wounded hand of the crucified Christ. On its fingertips are representations of the Holy Family. The infant Jesus' position on the thumb represents his importance, since much of a hand's function depends on the thumb. The red marks on the palm represent Christ's wounds from his crucifixion.
The five figures are the young Christ, his mother the Virgin Mary, his earthly father St. Joseph, and St. Anne and St. Joachim, Mary's parents. The inclusion of the extended family reflects the Latin American and Spanish regard for the family.
Can you tell me something interesting about this painting?
There are so many symbols embedded in this painting. The symbol of the hand derives from the European cult of Saint Anne. It also bears the wound of the stigmata in reference both to the Crucifixion and to the life of Saint Francis. The chalice (similar to a goblet) is filled with Christ's blood, and the seven lambs drinking from it derive from the Book of Revelation. The figures on the fingertips are Christ, his earthly parents Mary and Joseph, and his grandparents.