Do they build a new parliament?
Otherwise many thanks for describing the german vote system.
Looks pretty reasonable to me, it allows local out of party candidates to be elected, gives proportional representation to country-wide small parties and fair share for "big" parties.
Are there any cases where the election results were considered "unfair"?
The parliament is in the renovated Reichstag building, i.e. where the Bismarck era (and later Weimar era) parliament was seated. It has enough room for extra seats; especially since the theoretical minimum number of winnable seats was reduced from 656 to 598 (from the 2002 elections).
Regarding elections considered unfair: I don't recall a grave case, but there have always been murmurings over even small distortions. One thing I remember clearly was election night in 2002, when the result was narrow and it turned around during the night, and IIRC around midnight, there was a phase when it seemed the CDU/CSU got more votes but less mandates than the SPD due to the overhangs. (But in the end, SPD was ahead by a legendary 6.027 votes, and while SPD was ahead by 3 overhangs, the 8-seat difference of the potential coalition partners made the difference.) *Traitor*, n. A benighted individual who perceives an illusory distinction between serving his nation and abetting the criminals who govern it.