Dana Angluin's L* algorithm - Hypothesis inconsistent
I have no idea what it would mean for a hypothesis to be inconsistent in this context, but the answer to your second question is: No.  You won't receive the same counterexample twice.

The teacher returns a counterexample $w$.  Here a hypothesis is a DFA (a regular language) and $w$ is a word that the DFA gets wrong (either the DFA accepts, but $w$ is actually not in the language to be learned; or the DFA rejects, but $w$ is actually in the language to be learned).  Angluin's L* algorithm constructs a new DFA that is correct on all of the counterexamples that have been returned so far.  Since this DFA is correct on all past counterexamples received from the teacher, we will definitely never get the same counterexample a second time.