Let me say again that I don't *know* for certain the answer to your specific question.
That said, if I had those two tanks, I wouldn't think twice about using those snails as feeders. In order for them to present a significant hazard to your fish a number of things would have to be true that are in my opinion highly unlikely:
1) The toads are generally under stress in their tank in a way that causes them to fear predation and release their toxins on a regular basis.
2) There are no bacteria in your biofilter (or anywhere else, since they would quickly colonize the filter given that condition 1 is true) that can break down the toad poison, which is after all just protein.
3) There is not enough water volume in your tank and/or you don't change water enough to dilute the poison to a safe level.
4) Puffer metabolism is affected by toad poison, but snails are not (ie the snails will not die when exposed to the poison).
5) Snails will ingest and store the poison without metabolizing it, so that their tissues are poisonous.
6) Toad toxin is actually deadly (in reality I think it just tastes bad and mildly irritates the eyes, though in fairness I'm thinking of what happens when a much larger animal like a cat attacks).
It would blow my mind if 1,2 and 5 were all true. If it really worries you put some carbon in that filter. It will absorb pretty much all the toxins you're worried about.
As far as what the snails are eating, I think the shallowness of that water explains a lot. You're effectively feeding the tank light. A few toad turds and a lot of light means algae growth on the bottom, even if you don't see it because the snails keep it eaten down. You've also got a relatively large volume of substrate leaching nutrients and especially calcium into your water. In a deeper tank the algae growth will be less because more of the light is absorbed by water, and more conventional fish tanks typically have a pretty inert gravel substrate that doesn't provide much to the water, while I'm guessing you have actual soil in there.