1st I don't have the problem with the DoT fall off, They both continue ticking after the effect of Soul Harvest. (I have Crippling Death)
2nd some monster seems to take more damage by this effect than other monsters for some reason (maybe It's a bug?).
But for me, they always take damage.
3rd It's work fine with any kind of monster, Goblins including.
Maybe the thing you should consider is the area of effect of Soul Harvest and your latency.
Soul Harvest has a bit narrow AoE (12 yard I think).
With some monster that always running around like a tiny mobs or Goblin and a bit of latency gap can cause them to out-range your Soul Harvest area before the skill resolve.
about the 2nd question, from my observation, the same monster types tend to have different health pools. the difference can actually be pretty significant.
dont remember what difficulty it was, think it was t6 and i was in a rift with lots of khazras. some had 17million HP while others had well over 60million.
also you should get a quezacotl for your jade harvester, from what i have heard it basicly double or tripples your jade harvester bonus dmg because it only damages for 1 minute and not the full 5 minutes of creeping death.
Your 2nd point is easily answered, it has to deal with the crit mechanics of dot skills. If the first tic crits, the entire dot will crit. If the first tic does not crit, the entire dot will not crit. The times you feel like you arent doing any damage is because you are activiting soul harvest on a dot which didnt crit.
For some more clarifcation, Quezacolt will doube your damage as it doubles the rate of the dot. Creeping death makes your dots last 5 mins but Jade Harvester's soul harvest will only consume 30 seconds of it. It's done this way to balance it, or else if you'd consume the entire 5 min dot, you'd one shot everything.
Regarding treasure goblins, be aware they have a brief period where they are invulnerable. After you initially hit them, they wont take any damage for 1-2 seconds immedietely after. Make sure you arent hitting your soul harvest during this time.