Ten years passed, and this criminal died sometime in the interval, but not before telling his colleagues about the map. Father then showed up at Mother's house to get said map. He lied and told her that if she tried to call the police or intervene in any way, his colleagues (who he claimed were close-by) would kill her and the boys. Feeling confident that he had successfullly intimidated her, he then went to sleep right in her house. Mother kept the map all these years because she knew that he or someone from the gang would come looking for it, and she was afraid of what would happen if she no longer had it.
Father invited the boys on the trip to (unbeknownst to them) act as hostages to make sure that Mother didn't call the police after he'd left (and to make sure that she hadn't given him a fake map). This is why Mother looked so scared throughout the movie. Father, however, has a Hair-Trigger Temper, and nearly sends the boys home despite the fact that he needs them as hostages; whether from cooling down and coming to his senses or from orders received from his colleagues over the phone, he changes his mind and stops the boys from going back home.
At the very end, he seriously was contemplating killing Andrei and Ivan because he no longer needed them (as he now had the box). When he held up the axe to Andrei, he really was about to attack him with it. When he chased Ivan up the tower, he was only pretending to suddenly care about him in order to coax him down. Luckily for Ivan, Father slipped and fell to his death; however, since they never knew for sure that he was evil, his death feels like a tragic loss to them, rather than a triumphant victory.
Father and Mother had two pictures taken, one with Father and one without him. Ivan and Andrei only ever knew about the one with Father. Thus, when they see the picture in the car, they mistakenly believe that Father was supernaturally removed from the picture.
Now as for what the symbolism and religious references mean in relation to all this, Father is simply a counterfeit Messiah, a symbol of false, dashed hope; considering the movie is a study on troubled father-son relationships, this fits rather well. Father shares some similarities to the Biblical account of Jesus (the way he appears in his very first scene, his having eaten a lot of fish once), but it quickly becomes clear (to Ivan, but not to Andrei) that, where it matters, he is the exact opposite (the most blatant example being how he becomes angry with the boys for forgiving somebody; clearly a striking contrast for anyone who is familiar with the New Testament). The movie seems to basically be saying that we should be careful who we admire; there are those who are not to be trusted or followed, and Father is, by all appearances, one of those people.