op amp simulation issues

1. how to simulate input-refered offset ?
we know there are systematic offset and random offset.
If i simulate the opa in a real-used loop, while all the nodes' voltages are set through feedback, does the input differential voltage in this case equal to the systematic offset?
And is the random offset given by monte carlo analysis ? what's the meaning of nominal offset and average offset, which is more useful in design or application?

2. how to simulate the output noise voltage and input-refered noise?
i've heard that the noise of a amp mainly comes from its input-noise, which is mostly determined by reference voltage, such as bandgap. So i want to know how to simulate the bandgap's output noise? can someone give me some useful references ?
and whether should we consider about the noise in our design?

3. the common mode input and output range
Allen's book gives us some samples about common mode input and output range simulation.
But i think the unit-feedback scheme of CMI simulation can only be available if the upper limit and lower limit of output range cover the limits of input range. But it is not real in most actual circuits. so how can you simulate the actual input range and output range?
And how do you define the boundary of common mode input range if a unit-feedback scheme is used? when the input differential voltage is 1mv? or 100 uv? can you give me some reasonable reference?

Thank you very much, we can talk more about this topic if you are interested in it.

go for the book cmos analog circuit design by philip allan and holberg.
every thing is given regar ding the test setup for opamp

about the sim of the common mode input range

u can use open loop op-amp with a reasonable input common mode voltage with AC=1 in positive input and the same input common mode voltage with a small differential offset voltage at negative input. Then u sweep the small offset voltage to get a reasonable AC DBgain. With the small offset voltage u may sweep the input common mode voltage to have the common mode input range

Added after 3 minutes:

about the sim of the common mode output range

u can first determin a input common mode voltage, then sweep the small differential offset voltage at negative input to get reasonable output DBgain. With the smallest and the largest offset voltage, u can have the common mode output range at certain input common mode voltage.