Is there any pattern in this (e.g. Once per five years)?
Is it a sliding window?
2026-03-25 17:45:08.1774460708
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How often will the same date be on the same day of the week?
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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.
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