I think the children are being held in a different part of the island, separate from the rest of the others - Ben, Juliet, but they are still part of the same group. Remember, Ms Clugh had Walt and he said that they "made him take tests" and he was able (apparently) to get to a computer and see Michael's typing and write back to him. They must be held in another "hatch" with computer access.. Like they are at school. Maybe also where Alex had run away from - they took her back there later.