Regarding taking churched or baptised infants into the altar area: The proper custom is that males are taken by the priest into this area, including a "lap" around the Holy Table. Girl babies are placed by the priest on the top step of the ambon, in front of the Royal Doors (in Slavic custom), and "collected" by the child's mother; in Greek custom, the priest does not take the girl into the altar, but hands her back himself to the mother on the top step of the ambon.
Why the difference for boys and girls? Females, as a rule, are not permitted to enter into the area beyond the iconostasis. This should not be seen as "discrimination" in the modern sense, it is simply the historic Holy Tradition of the Orthodox Church. This is why you'll never see "altargirls" in an Orthodox church. There are a few specific exceptions, however, such as senior abbesses who have been given a blessing to do so by their bishop, and for certain other very specific situations. The church I have been attending for the past decade was painted with icons on the walls and ceiling by three iconographers, two monks, and a laywoman. The icons in the curved apse of the altar area were painted by the woman, who had a particular talent for painting on curved surfaces. She was given the authority to do so by her bishop, who was no liberal softy, I might add.