unfamiliar gain equation of differential amplifier
gds = 1/rds => conductance add up when you have parallel resistances.

G = 1/R

R1 || R2 = 1 / (G1 +G2)

Thus, rds2 || rds4 = 1/ [(gds2 + gds4) ]

So, GAIN for the first stage;

Av = gm2 * (rds2 || rs4) = gm2 / (gds2 + gds4)

here since  m1 and m2 are differential pairs ,its ok to assume that their
 trans conductances are almost same (gm1 =gm2).

Part2:

Regarding the expression in terms of current ,

The drain resistance (rd) is due to channel length modulation and is given by :

rds = 1/ (lambda * Id) or gds = ( lambda * Id).

So replacing gds, we get;

Av= gm2 / [lambda*(Id2 + Id4) ]