Yes, Alizarin is certainly the most popular fugitive pigment. Natural madder is even worse. They are significantly more permanent than Alizarin, but perhaps not quite permanent enough to be called permanent. And, their properties are not often similar. No it is not, do your research.
Insoluble mercury is a whole different matter.
I haven't died yet. And, some have said that dentists are scaring people in order to get them to come in and get them all replaced. The source you posted is similar to those I have read. Organic mercury is extremely dangerous, yes. I've said that.