What if you alter a differential amplifier by giving it a positive feedback rather than a negative feedback?
Answers to your other questions can be obtained by solving for the last question.


  How to derive the equations for this type of a circuit?


A fundamental property of an ideal opamp is that it has infinite gain. In the case of negative feedback that means it's two inputs are at the same differential.

In the case of positive feedback that means the output is either at the highest or lowest output levels. Typically Vcc and Vee. 

In this case assuming that vout is at one extreme, holding v2 constant you can find the v1 that will switch vout to the other extreme.  You will have two such points, depending the initial state of vout.