Amplification of signal in a circuit. Is my calculation ok?
This is (for the time being) more a comment than an answer.

The first KCL equation should be:

$$(V_x - U_{in})g_{be} + (V_x - V_y)g_{ce} + V_xG_e = (U_{in} - V_x)g$$

which simplifies to:

$$V_x(g_{be} + g_{ce} + G_e + g) -V_yg_{ce} = U_{in}(g_{be} + g)  $$

For input resistance, find the current through \$r_{be}\$ which will be in terms of \$U_{in}\$.

The input resistance is then easily found to be:

$$r_{in} = \dfrac{U_{in}}{i_{r_{be}}}$$