Technically your school rank doesn't affect your uai.
However, it is important in predicting from school marks since different school have diffreent assessments. Also, outside 120 schools would have weaker students.
In regard to HSC marks, rank of school shouldn't matter. However, the competitiveness of higher ranked schools would boost your marks a little.
You get mark 18/12/2003, you get UAI 19/12/2003
Main round offers start 5/1/2004