Do chemical garden coral formations leach toxins? Short version, I want to make a coral garden with sodium silicate and salts, and I would like to put that in my fish tank, but I'm concerned about the fish getting poisoned.

https://en.wikipedia.org/wiki/Chemical_garden
https://www.thoughtco.com/make-your-own-magic-rocks-607653

The above pages describe the chemicals needed. The articles say that once the corals have formed, they can be rinsed to remove the sodium silicate, and kept in fresh water. Most of the articles I've read say the same thing, in different ways. But none of them say whether the coral degrades, or if it is stable.

Are there experiments that I can do to test this? How can I be sure?
Experiments to test if toxins leach from silicates do exist; however, these experiments involve dangerous chemicals.  For that reason these tests should be left to qualified lab personnel and not described here.  Performing these experiments are expensive and would need to be performed on every combination of methodologies to make a "chemical garden".  Because so many combinations exists, quality control on such an experiment would be difficult.   

Experiment aside, a "chemical garden" in a fish tank is a bad idea.  While silica is chemically insoluble,  it can be converted biologically into orthosilicic acid.  This form of silica is soluble. This process in nature is called biological weathering.  

Chromium, lead, and perhaps some of the other compounds are carcinogenic to humans.  These compounds, even in an immobilized form, are not worth the risk and should be nowhere near a fish tank.