Do simulation, you use voltage source to bias MOS M7 that maybe lead the output pull high or pull low (without gain) when you do montecarlo. M7 should a current source relate to I1.
For a Amp the M1 M2 need large Gm but M3 M4 need large Rds so the size of M3 and M4 should be small.
In your circuit, the C1 is too large that can not integrated in chip.
For so large value 50U, R5 is 0, maybe your circuit is stabe.
For the 2 stage AMP you shoule analyse where is first pole, where is second, how much loading. If you loading is very large cap, you don't need miller compensation at that time the miller maybe is not good for stable.
If you want to learn how to design AMP:
First you should analysis the amp, not to do simulation.
Calculate the pole and zero first.
And you should know what the gain, bandwidth etc you needed. from that get the tail current value.
Then give a current source as bias (example use the current source replace R1 in your first ciruit)
Then make the M9 and M10 is saturation (give a 0.2 Vod).
The M1 M2 can in stauration or cutoff region (need larger size). the M3 and M4 need larger Rds (small size).
The miller compsenation must relate to output loading.