Signet of Malice & Hastened Replenishment
Very likely not, it doesn’t trigger other on-heal effects and it would be way way OP for that one.
It doesn’t. In GW2 for the purposes of “on heal” triggers the only thing that really counts is actively utilizing a heal skill. As Frans said, it’d be utterly broken if an effect balanced around (at minimum) a 12 second CD was able to be triggered off of an effect that can go off a dozen times in one second in some situations. You’d have literally unlimited initiative all of the time.
If you have Signet Use and Hastened Replenishment, you can get 6 initiative from activating Signet of Malice (12 second cool-down).