I have not so much experience to design on-chip balun, but I believe the basic principles are the same. As I know three-port balun is always single-ended on one side and single-balanced on another. For three port device it is impossible to have two balanced signals on the other side of the balun. The balanced output signal can be represented by two vectors that are equal in amplitude and opposite in phase (180 degree phase shift). The amplitude and phase imbalance are important balun parameters and should be kept minimal. I cannot tell you about MIM capacitors because I never use them, but I will ask about it our IC designers. May be they know what it is and why this caps are used. In lamp element designs I never saw or used capacitors to tune the balun. For me it is very strange. Any reactance in balun circuit are parasitic and must be avoid.