Small signal model multistage amplifier
I have tried to analyze the circuit (without using the small-signal equivalent diagram). At first, it is necessary to calculate the DC quiescent currents in order to find the corresponding transconductances gm=Ic/Vt for both transistors (gm1 and gm2)

Here is the set of equations I have found:

Vcc-VB1=RB1(IB1+I1) with I1=VB1/R2

Vcc-VB1=RB1(IB1+VB1/R2).

VB1+0.56+0.71=VE2  >>>  VB1=VE2-1.27volts.

VE2=Vcc-IE2*RE2

IE2=IB2*200

VB1=Vcc - IE2*RE2 - 1.27volts.

IE2=IB2*200

VB1=Vcc - IB2*200*RE2 - 1.27volts.

with IB2=I1-IE1 with I1=(Vcc-VE1)/RE1

IB2=I1-IE1= (Vcc-VE1)/RE1 - IE1

IB2=(Vcc-VE1)/RE1 - IB1*200

VE1=VB1-0.56volts

IB2=(Vcc-VB1+0.56)/RE1 - IB1*200

Result: Three equations (in bold)for three Unknowns: VB1, IB1, IB2

(I hope, I didn`t make any errors)

After Ic1 and Ic2 have been found (and the corresponding values for gm1 amd gm2) it shouldn`t be a problem to apply the well-known gain formulas.