Advanced theory of individual economic behaviour in production, consumption, and general equilibrium. Are these topics useful to study environmental economics a the graduate level, or is there not a lot of overlap?
It depends on what you like to do in environmental economics. There are lots of people who are working on moral hazard issues on environmental economics by principal-agent models.
More specifically, an interesting question arises from non-point source pollution. Let's say farmers are using pesticides which cause pollution. Probably, you don't know specifically which of farmers are responsible. How could you create "incentives" in order to avoid this situation(pollution) ? You can look at the Segerson (1988), published in Journal of Environmental Economics and Management in order to understand this issue more precisely.
Another field could be about social choice theory (and decision theory) in environmental economics, especially on equity between individuals and generations. These issues can be included in microeconomics but more in applied math as they use topology etc. (Geir Asheim, Stéphane Zuber's papers could be interesing for this subject.)
Just to finish, I think there are more things to do in environmental economics at a macroeconomic level. (Note that my opinion could be biased as I am working at macro level.)
Microeconomic theory is relevant to many topics in environmental economics, eg pollution control, valuation of environmental goods, economics of natural resources. A knowledge of more advanced theory would enable you to go more deeply into such topics and understand more of the literature. However, you can get quite a long way in environmental economics by applying basic microeconomic theory to situations with environmental features such as negative externalities (pollution), non-market environmental goods (many parks) public goods and "bads" (climate change), renewable resources (fish, forests) and non-renewable resources (minerals).
If you are considering taking a graduate-level course in environmental economics, I suggest you look at the detailed content of particular courses to get an idea of what previous knowledge is assumed. I took an MSc in environmental economics several years ago which included a module on "economic principles" - essentially basic microeconomics, and obviously designed so that the course could be offered to those with backgrounds in related fields such as environmental science or agriculture but no previous study of economics.