How to calculate the transconductance of this circuit?
This is an operational transconductance amplifier (OTA).

The transconductance of the OTA is rather a complex calculation if you want
the large-signal model, and takes a few pages to set up... the difference transconductance of the T1-T2 pair is a hyperbolic tangent, with temperature dependence, and that propogates to the output.

See _Analysis and Design of Analog Integrated Circuits by Grey and Meyer for a discussion (chapter 3 section 4).

Common mode input R will depend, I suspect, on the Early voltage of T10.  Make a Spice model, with realistic transistor specs, to solve the various parameters.