TRIAC won't turn on/turn off
Usually the problem is that you have swapped MT1 and MT2 on the triac.


  ... depending on R3 (I've read somewhere that it's necessary if triac is sensitive) - if I plug this resistor, triac is always on, but if resistor isn't there - triac is always off. 








simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. (a) What you intended. (b) What you've done.

The gate needs to be connected to MT2 to turn the triac on. Your R3 test confirms that this is the error. Your opto-triac is connecting the gate to MT1 and so it does nothing.