Do I need trivial resistor or not if V/I = zero or almost zero
You can try to do this with the buzzer, but you have no idea what  current the buzzer wants.  If it wants 15 mA, have a field  day and give this a go.  You won't need the resistor.  You can try it, anyway.  Even if the numbers aren't perfect, you'll either hit an equilibrium point where the buzzer load line intersects with the LED curve, or you won't forward bias the LED enough to make it turn on, and no current will flow.

I recommend wiring the buzzer and resistor in parallel, assuming you won't pull too much current from the Arduino pin (checking this is on you!).  If you're pulling too much current, use a transistor.

If you want 15 mA going through a 2V LED, you need to drop 3 volts.  

$$R= \frac{3V}{15mA} = 200 \Omega$$

You'd use the same calculation for the 2 volt drop you want for the buzzer, after you figure out how much current it needs.