Balun design analysis

For Analysis and Design of Miniaturized Lumped-Distributed Impedance-Transforming Baluns ,

1) Why use admittance Y (or 1/Z) instead of impedance Z ?

2) What is T_even ?

1-When you analysis the circuit with Short Circuit Conditions, Y-Parameters are useful.
2-Balun Circuits can be driven ODD Mode or EVEN Mode e.g. Driving Currents/Voltages may be In-Phase ( Even Mode) or Out-of-Phase (Odd Mode) ( like Parallel Coupled Transmission Lines ) therefore there are 2 Characteristic Impedances.ODD Mode and EVEN Mode, so there should be 2 set of Reflection Coefficient/Transmission Parameters/S-Parameters.

Do you have any guide on how to derive expressions (2a) and (2b) in the paper ?

You can find lot of information about Transmission Lines here..
https://www.ece.rutgers.edu/~orfanidi/ewa/
Also, there are tons of paper about them, seek internet..

I am reading another paper by the same author : Analysis and Design of Impedance-Transforming Planar Marchand Baluns

What does it mean by "coupling factor, C" in equation (1) ?

And how to derive equation (2) which is basically the S-parameters matrix of the Marchand balun by using Figure 1 as suggested by author ?