Summary of my Answer: Your first sentence is OK. Your last sentence (with "even") sounds odd (no pun intended).
I will comment sentence by sentence.
(1) Your first sentence sounds OK and means that he did not act as a leader should act.
As a leader, he did not act accordingly.
(2) My confusion comes with your second sentence:
Even though he was the leader, he did not act accordingly, as he has all the time.
This could mean that he has never acted as a leader, or it could mean that he usually acts as a leader, but not in this one case.
If you meant that the leader has never acted as a leader, say: "Even though he is the leader, he has never acted as a leader should act."
Even though he is the leader, he has never acted as a leader should act.
If you mean that the leader has, in one instance, not acted as a leader, say: "Although he is usually a good leader, in the case of X he did not act as a leader should."
Although he is usually good leader, in the case of X he did not act as a leader should.
(3) I cannot understand your third sentence:
Because he was the leader, he did not act accordingly and was supposed to do so (was supposed to not act accordingly.
(4) As for your fourth sentence:
Even as a leader, he did not act accordingly.
This sounds odd. There seems to be something missing; you need to be specific.
The first sentence says he didn't act as a leader should act. Vague, but OK.
The fourth sentence says Even though he was a leader, he didn't do X. The fourth sentence, with "even" implies that he didn't do something that we would expect from non-leaders, as well as from leaders. For example, because this is a family situation you might say: "Even as a leader, he did not set a good example for the children."