Differential stage Av value with current sources
You have mentioned the expression Ad = Rc/re.

Please note that this expression is (1) a very rough approximation for a common emitter amplifier with heavy negative feedback (due to re) and (2) does not apply for a diff. amplifier. Neither for a simple one (two or three transistors only) nor for the one shown by you.

This is because the resistance in the common emitter path (as seen from the left transistor of the diff. pair) is bypassed by the low-resistive input of the most right transistors emitter.

For a good understanding of the various gain expressions (common mode, single diff. mode, full diff. mode) you must know the working principle of the diff. pair. 



Detailed derivation (for the diff. stage Q1, Q2, Q3 only).

Assumption: Unsymm. differential operation with Vin1=Vin and Vin2=0 [Q1 can be treated as an emitter follower loaded by the input resistance of Q2 in common base configuration].

Gain: Ad=Gain1*Gain2=A1*A2 with

A1=gm1*ro/(1+gm1*ro) with ro=re||(1/gm2). 

If the dynamic resistance re is very large (re>>1/gm2) we can set ro=1/gm2.

A1=(gm1/gm2)/(1+gm1/gm2).

For identical operational points for Q1 and Q2 we have: gm1=gm2=gm and the gain is

A1=1/2.

Hence, with A2=gm*Rc (Rc=collector resistance) the total gain is

Ad=0.5*gm*Rc .