Hi,
Why don't you try the folded cascode arch with telescopic load, you can improve the gain as well get a good ICMR or the swing.
The answer for you first question, my guess is (which means I don't understand completely), the transient accounts large as well as the small signal parasitics, where as in the ac simulation the circuit is considered to be DC stabilized and only the small signal equations are solved.
Others please correct me if I am wrong.
Regards,
RDV