How do I solve for the gain (MOSFET+Capacitor)?
The most direct way is to use nodal or loop relations. 
1) (Vin-Vx)*C1*s=(Vx-Vo)*C2*s
2) (Vx-Vo)*C2*s=Vxgm+Vogo
Eliminate Vx. Answer above is low frequency so let s->0 in solution.

Full solution is
Vo/Vin=C1s{1/(C1s+C2s)}(C2s-gm){1/(go+C2s)}/{1-C2s*{1/(C1s+C2s)}(C2s-gm){1/(go+C2s)}
where go=1/ro with gm models the mos transistor

Cancel out 's' terms in cap division factors, drop out C2s in (C2s-gm) factor and finally let s=0 in final to get solution you are looking for.

The full solution is best found using dpi/sfg as shown in Feedback in Analog Circuits by A. Ochoa