What websites or other ways to query or determine the properties of inorganic substances, especially toxicity?
We are not an authority on toxicity of inorganic materials, and the Materials Project does not offer this information.
Here are some resources that might be helpful, but I would encourage independent research:
European Chemicals Agency
PubChem (NIH), search engine including chemical toxicity
National Institute for Occupational Safety and Health, pocket guide of chemical hazards
See also http://www.ilpi.com/msds/ and https://ucsd.libguides.com/safety/government for links to other resources. In particular, many commercial entities have databases of materials safety data sheets (MSDS) such as Sigma-Aldrich.
Hope this helps,