I pretty much exclusively play Assassination, haven't even bothered trying the other two yet and was just wondering how the legendary ring effects garrote?
I'm not sure to be honest. I just got the ring as my first legendary a few days ago and didn't even think of this. I'm actually embarrassed to say this but I don't even know if garrote does damage immediately like if the first tick of the bleed is immediate which I think it may be in which case it probably does 30% of that amount as shadow damage.
Insignia only works on Mutilate. Whether that's a bug or a design decision, I can't say. Hopefully it works on Kingsbane too in 7.1 when it gives a combo point since it has a direct damage component.