To answer your first question: no. The Belgian crisis has been entered into the Guinness book of records as the longest time a country has ever taken to form a government, and it has not been 'bested' since.

To answer your second question: concerning the Belgian crisis, you have to understand that forming a government easily takes up a month or more in the Belgian system even without a crisis. This means that we do have a system of a government of "running affairs", which means the previous government still continues to function, but only in a limited way - no new proposals can be enacted, but current and immediate problems can still be dealt with.