Don't worry! There is no sure thing as 'lower rank'. I know so many cases that even thier brother and sister are studying in the school, the kid still got rejected. On the otherhand, many children without 'special talent' who are supposed to be not related to school still got admitted. I think the interview performance is extremely important.
I don't think there is any relation about the timing of receiving letter. Some first "in" have already been conducted thsi morning. Parents do not need to be interviewed.