Foucault, power, and the baby bird

I am not an expert in Foucault. I have not even read any books by Foucault; I plan to, but I have not yet had the time. I will make the time, but not yet. As a non-expert, I have had to borrow what I know about Foucault and his idea of power from lectures and the internet. I understand that a book would be better, and reading said book in French better still, but I don't know French, and I haven't had time, so here is a summary of Foucault's definition of power cobbled together from the lectured internet:

1. power is not a thing but a relation
2. power is not simply repressive but it is productive
3. power is not simply a property of the State. Power is not something that is exclusively localized in government and the State (which is not a universal essence). Rather, power is exercised throughout the social body.
4. power operates at the most micro levels of social relations. Power is omnipresent at every level of the social body (http://www.michel-foucault.com, 2012).

 I love the first definition, "power is not a thing but a relation". I can never have power, nor take power, but only exist within power. For someone born into a capitalist society, this is a real paradigm breaker.
Foucault would argue, I believe, that students listen teachers because they are locked into a discourse which values teachers as a source of information to students. This discourse is power.
I wonder why substitute teachers have such a difficult time in a new classroom, like myself and incident with the baby bird. Power, according to Foucault and the internet, is present in all levels (macro and micro) of society, but is it to a greater or lesser extent? If power is a relation, then are the relationships between students stronger than teachers. Why would this be the case? Society has said that students are to listen to teachers, but if there is no relationship, like when a new Sub teaches a class, the students have will find it difficult to listen. Are there hierarchies of power? Can hierarchies of power exist within Foucault's framework? Does Foucault give us the whole picture?