1: True only if your power supply is symmetrical (-vdd +vdd).
Note that V+ - V- = 0, but V+ != 0 and V- != 0 else your opamp is not biased (again, for non symmetrical power supply, and will simply not work.
2: Seems correct for b.
For c, seems correct too, but like Vov4 and Vov2 depends on Vin.
In d, this is a small signal analysis model, M1 and M2 are not biased, and Vout (in open loop) depends directly on these gate voltages !
Try to simulate a simple opamp (like d) in open loop first and look at Vout, then in a "buffer" configuration (vout looped on V-, input on V+, and add a dc source on V+, you'll learn a lot !)
3: It depends what you are looking for !
If you want frequency analysis or loop stability analysis, small signal (ie ac analysis) is ok. But it does NOT mean that the small signal variation are centered around 0 V !
If you want distortion analysis, slew rate, etc, you'll need spice model (or equivalent time model)
Hope this will help you