I doubt that the frogspawn would have killed the hawkfish. The other way around is much more likely, with the coral staying closed and not getting enough nutrients. Even if we decided I'm wrong here, and this did kill the frogspawn, that would explain the coincident deaths of the other fish. Going by Occam's Razor, I'd be inclined to reject this hypothesis.
I'm not sure about the surgical gloves issue. Many gloves that are listed as "powder-free" are not truly powder free (in the same way that many fat-free foods aren't truly fat-free). Many of them have to be very carefully examined to find evidence of the powders, but it's often there. So that's one potential source of trouble.
The other is the boiling of the skimmer parts (I'm assuming that you meant boiling, and not "bowling"). I doubt this was necessary, and probably puts some of the plastics at temperatures they're not really designed for. This could potentially create some by-products that could leach into the water and wreak havoc.
You said you gave your hands a good wash. With what?
Do you every use Purell or other similar alcohol-based hand-rinses? I know of several tank crashes that have been traced back to these (including one of my own a few years ago). I don't know what in the product causes the problem, probably a residue that's left on the hands after the rest of it has evaporated. The problems are not too different from what you're describing. Basically all the fish look fine, then look dead or near dead in a very short while. All of the parameters test out fine. The corals look OK (not perfect, but OK), and then rebound, and the motile inverts seem to not be affected at all.
Another question. When you added the skimmer to your refugium, did you disturb the sediment in it at all, or have to move any substrate to fit the skimmer in?
It's possible that there were anoxic areas which released hydrogen sulfide when disturbed. That can certainly be toxic enough to cause the fish to die.
I think there are several plausible explanations that are much more likely than the superglue to be the cause of the problems here, based partly on the fact that thousands of us have used the stuff underwater without problem. I even know some people who have done all of the steps of supergluing frags underwater. I personally think this is more cumbersome and difficult, but I've seen it done. Anyway, the point is that they've been able to do it with no ill effects.
The conflicting info comes from the fact that your post about the frogspawn says, "now I am short one fish". This does contradict your other posts, which suggest you're short 3 fish. This may just have been poor wording.
Dave