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.

If you mean that the leader has, in one instance, not acted as a leader, say:

> 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."