I don't know how to answer this question without further clarification. Methane, CH₄, is a gas at room temperature and I am not aware of any organisms living "in methane" which I would read as organisms living "in water" - liquid methane would be way too cold for life to exist in it. Or does he mean in methane as opposed to "in air"? In that case, anaerobic organisms can do that, and I could maybe write something about that. The question there would be more "how can organisms live without oxygen", because methane is not much different from say nitrogen or any other gas that is not oxygen in its effect on organisms. In principle, methane could be a source of "food" (it is the main component of natural gas) but I am not aware of organisms that make use of that and they would surely require oxygen. There are also some organisms that produce methane as part of their metabolism...

They don't, really - methane is a gas, and at the temperatures where methane is not a gas, water is solid.

That said methane really isn't that poisonous. It's more that it's not oxygen than that it's methane, and some bacteria are capable of combining methane with oxygen to get energy (as well as waste products of carbon dioxide and water).