Kripke automaton and observations
Your answers seem correct.
As for 2: one way is to simply check, a quicker way is to observe that all states go to A upon reading 1, so the sequence 001 ends in A, and A satisfies "red".

3 can be solved by the test "blue" (without any moves) and 4 can be solved with the test "red".

As for 5: in order to show that no test can differentiate B and D, observe that for the letter 1, both go to A, for the letter 0 both go to C, and both have the same light (blue). Thus, you can say that the "language" of both state is equal.