No, they mean Carbon and anything else they can to sick on the wall. They even got the Supreme Court to agree with them about Carbon the same time Defense of Marriage fell +/- a few years or whatever my memories are capable of...
No they don't. The first line of the article says tax fossil fuels. Fossil fuel comes in many different forms of carbon or carbon containing compounds or organic compounds. Organic chemistry is the study of carbon containing compounds, and there are 19 classes of organic compounds.
Fossil fuel can be a very simple carbon compound like methane or something complex like peat.
You definitely don't want to tax CO2 because there are other sources of CO2 besides fossil fuel.
Likewise, you would want to tax ethane if it is used as a fossil fuel but not if the ethane is used as a raw material for polyethylene.