Are accepting states and unaccepting states distinguishable?
This depends on your definition on distinguishable. Let's assume the following definition: $A,B$ are distinguishable if for some word $x$, if the automaton starts at $A$ and reads $x$ then it accepts, while if it starts at $B$ and reads $x$ then it rejects; or vice versa.

Under than definition, any accepting state is distinguishable from any non-accepting state: just take $x$ to be the empty string.