"Did they baptize only believers by immersion? Probably not seeing that would muddy the drinking water or worse."
Well, they were all Orthodox so of course they baptized by immersion! None of that sprinkling stuff for us! As for the water, well, they were Fathers, so the water never, ever, got muddy; It always stayed cool and clear. :)
Seriously, there are very many stories from the Desert Fathers about the pools near monasteries and how they would dry up when the monks got "rowdy" or forgot their obligations and returned when they got back in line. The presence of sweet water for those guys out in the Egyptian or Judean desert was a big deal as you can imagine. The water works they set up near the monasteries and even more so near the "cells" of hermits are impressive. The remains of them can be seen in many places over there, particularly on the flanks of Mt. Sinai above the Monastery of St. Katherine.
When my grand nephew was baptized in the Greek Orthodox Church, as a baby, the Priest held him up naked and pronounced the first words of consecration, but when he tried to immerse him the baby grabbed both side of the baptismal font and started screaming. The Priest and every one there laughed for a while, the baby stopped crying, and the Priest started again with the words of consecration and tried to immerse the baby again. Again the baby screamed and held on to both sides of the font. The Priest was a little perturbed and embarrassed so he spoke softly to the baby trying to calm him down. The baby stopped crying and the Priest once again held him up and said the words of consecration and again the baby screamed and held on to the side of the font and the Priest recognizing the inevitable took a little water in his hand asked for forgiveness and sprinkled the boy to the applause of the congregation.