Differential gain of an op-amp and feedback
A is unimportant. For an actual opamp the A can vary heavily. 9000 vs 11000 so basing your small signal gain on this number is a bad idea.  

in an actual circuit A just needs to be sufficiently large so that we can make the valid assumptions in order to calculate the small signal gain based on the negative feedback applied. Here is how you do that. http://www.radio-electronics.com/info/circuits/opamp_basics/operational-amplifier-gain.php

As far as startup conditions, You haven't gotten that far in your class to see the full opamp circuit which looks more like this. https://i.stack.imgur.com/U9Gr4.png
As you can see on startup the output is (close to) high but really its startup value is unimportant. This initial value then propagates through the negative feedback path and presents its input to the opamp. then the differential (v1 - v2) is amplified by A presenting a new output which is then propagated through the feedback path again. Parasitic capacitance keeps the output from changing instantaneously which prevents oscillation from occurring with a linear feedback network, such as a resistor network.