Two-stages class AB amplifier
Q2: when voltage at gate M1 is increased then the drain current through M1, M3 and M4 increases that will pull up (increases) the voltage at the gates of M8 and M5. So M5 will conduct less current making the output voltage drop (decrease).

No need to simulate that :-) but if you want, confirm this by simulation.

So yes you're right, the gate of M1 is the inverting input.

Q1: because of that (written above) now the gain becomes positive.