The two VCVS are put there to preserve the symmetry.
V1 is the differential voltage.
E1 is used to +0.5 * V1 on the + node.
E2 is used to put -0.5 * V1 on the - node.
Then the differential voltage appearing accross the + and the - terminal
will be V1 .
is the circuit hooked up correctly?
it seems theres -0.5 * V1 on the + node (Vinp)
and -0.5 * V1 on the - node. (Vinn)
The caps C3, C4 are there to provide an AC ground. It also allows the input gates
in the + and - nodes to be biased by the output voltage from vop and von, which is probably close to vcm (2.5) in this case.
Most likely, C1, C2 effects the location of the dominant pole in this circuit. Making C1, C2 bigger will shift the dominant pole to a lower frequency.
And thus making C1, C2 bigger will increase the phase margin of this circuit,
making it more stable. At the same time, if you make C1, C2 bigger, it will reduce your open loop bandwidth.