How do I calculate the resistor value for this circuit? Will this circuit allow buzzer to work?
One thing about your current calculation, a comment also mentioned it but that is to give you a rough estimate of the impedance of the buzzer, if you calculate you get 12/15mA which is about 800 ohms. Now this is not a straight up resistor and it is not exactly the same at all voltages, but as a rough estimate for current and voltage drop it should be close enough.

so assuming your LED is perfect you could get 3V at the buzzer, but since it is not this is not gonna happen you are not complying with the minimum voltage your buzzer wants(3V) so maybe it will not work.

LED forward voltage or voltage drop depends on many things, color is a big factor since you are saying 2V my guess would be that you are working with a red or green one. However, a blue diode drop up to 3.5V so if you have info on your diode look up its datasheet online and see the number for forward voltage.

what you need to do is provide 3V + Led forward voltage as the input to insure 3V are delivered at the buzzer.

because of that somewhere around 5V(add a bit of a safety margin) as the input would be best, you have 800 ohm as the buzzer impedance, it should draw about 3.75mA. I think that is enough for the LED to shine just fine(it will not be super bright), your voltage source needs to be able to provide this amount of power plus the losses on the diode(current will be slightly higher than the number I provided)

finally, there are cases would people add an extra resistor like you did, I will list some:

1) diode short circuits, this would cause the source to apply full voltage to the buzzer: since your buzzer can handle up to 24V this is okay.

2) buzzer short circuits and causes a current draw that could damage my voltage source or LED, here you add a limiting resistor that takes into consideration this possibility and limits current accordingly.

Hope your project goes well.