About OpAmp phase-reversal
Presumably you recognize Q1 and Q2 as a differential pair feeding a current mirror load Q3/Q4. 

The lower of the two differential inputs will cause the related transistor to hog most of the current so the collector voltage will rise- if the transistors remain in the active region. In this case the input voltage is applied to the non-inverting input so a lower input voltage tends to drive the output Vout lower. 

However if the input voltage drops below VbeQ5+VbeQ6+VsatQ2-VbeQ2 then the transistor Q2 will be saturated and the collector voltage will be below the voltage required to turn on Q5/Q6, so the output Vout will snap high. Since this is the reverse of the usual action of a non-inverting input, we can call this phase reversal.