A(p) holds in a state iff all infinite paths leaving that state satisfy p. Typically, p is not a state formula, but a path formula, since otherwise, A(p) would just mean that (E true) → p, i.e., if there are infinite outgoing paths, then p must hold in the current state. Since all infinite paths leaving the current state share the same initial state (which is the current state), this implies that the current state must satisfy p.
In your structure A(c) holds in s0 and s2, as you say, but also in s5.
E(p) holds in a state iff there is at least one infinite paths leaving that state that satisfies p. Again, if p should be a state formula, then it would mean (E true)∧p, i.e., there should be an infinite outgoing path, and the current state must satisfy p.
You may also recall E(p) = ¬¬E(p) = ¬A(¬p).