A) Does libertarianism necessarily entail the assertion, “all property rights are absolute”?
B) …or can exceptions ever be made under libertarianism?
C) …and if one stipulates no exceptions ever are permitted, then one is an anarchist?
Depends strongly on the context. For instance, if you need to break into a cabin in the forests where the owner is not currently present, you may do so, provided it is an emergency and you will compensate the owner for any damages caused. May a state violate property rights though? No. It is nothing but organized crime. The only legitimate thing the State can do is to do nothing at all. Roderick Long addresses the issue of property rights in his lectures, The Foundations of Libertarian Ethics.
Proper rights are not absolute. They are essential.