In Germany both, public holidays and school holidays, differ from one Federal State to the next.
Since KIT is in Baden-Württemberg, the Baden-Württemberg regulations apply.
This means that KIT is closed and there are no lectures on all public holidays. To find a current list of public holidays please check: http://en.wikipedia.org/wiki/Public_holidays_in_Germany and http://www.holidays-info.com/Holidays-Germany/holidays.html.
In addition, there are no lectures during the “semester holidays”: http://www.intl.kit.edu/istudies/3157.php.
School holidays DO NOT apply to universities, but only to primary and secondary education institutions: http://www.holidays-info.com/School-Holidays-Germany/2014/school-holidays_2014.html.