In the pattern 고는 하다 it means to do something habitually: I used to be surprised by that, we do say things like that to comfort them, in those cases you use a more casual polite style. In the other lines the 는 is simply added for contrast, setting one part of the sentence against another, as in the line meaning I do at least try to check right away. One line is the fixed 빼고는, meaning apart from.