How often will the same date be on the same day of the week? Is there any pattern in this (e.g. Once per five years)? 
Is it a sliding window?
 A: It's more complicated than that due to leap years among other things. Check out J.H. Conway's doomsday rule where all your questions should be answered in full detail.
See also the answer and the comments to this related question.
A: Mostly, in cycles of 6, 11, and 11 years. Leap years only repeat every 28 years. See http://wiki.answers.com/Q/How_often_in_years_do_calendars_repeat_with_the_same_day-date_combinations
A: All depends on the year it starts first birthday after you been born. If your birthday starts on same day , same date, same month. It will take 5 years,  6 years or 11 years which will bring you to your original day of birthday and the sequence never change. Sequence (11 6 5 6 11 6 5 6 11) all depends on which years sequence(5 6 11 6 5 6 11 6 5)or(6 5 6 11 6 5 6 11 6) you start your sequence, but it never change.You can test it yourself and see the consistency of the sequence birthday, same day of the week.
A: I found out: it is a sequence like this every 11-6-5-6-11 years (periodic), 11-6-5-11 years.
