You did not say what type of IC it is nor to what voltage the negative supply pin (Vee) is connected.
So I have assumed that it is a voltage comparator with an open collector output and that Vee is connected to gnd (0 Volt).
Now your questions and my answers:-
Q1. If R3 and R2 are low, then the output of the comparator is low? It could be High or Low depending on which state the bistable is in.
Q2. If we apply a 15 volt pulse to R3 won't the output still be low? Yes if it was initially Low.
Q3. Also if we apply a 15 volt pulse to R2 the output is still low? Ditto
Q4. The data sheet I copied the circuit from listed it as a bi-stable multivibrator?
It is a voltage comparator with hysteresis. So it can be used as a bistable if the input voltage (ie. at R3) is held normally between the threshold levels.
Q5. Once the output is low the plus input voltage will never get over about 5 volts? Yes if you limit the voltage at R3 to between 15 Volt and 0 Volt.
Q6. The minus input voltage will be either 15 volts or 7.5 volts? Yes, assuming R2 is connected to either gnd or +15 Volt.
What you are missing is that the voltage applied to R3 can go above +15 Volt or below 0 Volt.
My calculations show that the threshold levels are +22.2 Volt and -3.86 Volt - assuming that R2 is connected to gnd.
So when Vin (the voltage at R3) is > 22.2 Volt, the output will go High and remain high until Vin is reduced to < -3.86 Volt.
Thus the circuit acts as a Bistable if Vin is held normally in between the threshold levels (say at 0 Volt for example). Thus to set the bistable (ie. make Vout High), you must apply a pulse of > 22.2 Volt to R3. Once set High, it will remain high until you apply a pulse of < 3.86 Volt to R3.
If any of this is still unclear, please ask.
Len