You may be over-thinking things... A full moon symbolizes fullness, or in this case completion. It also symbolizes power, and thus the full moon symbolizes completion of power.
This is exactly, what we see. Obito is somewhat "complete", as he has become the Juubi's jinchuriki. So the full moon symbolizes this.
For the case of Madara vs Hashirama, the circumstances are a bit different, as we see the moon twice, and both times with the sound of thunder. Of course the moon could still symbolize completion, as it was here, that Madara obtained Hashirama's DNA, however, the significant sfx for thunder appears twice, as if "something" started and ended, perhaps a genjutsu. This may have nothing to do with the moon though.
Also the moon we see in the panel, where Obito goes crazy after seeing Rin is dead is a very different case. It's just a "random" moon, that Obito "sees" in the other dimension, because in the "real world" it is day. The fact that the Moon is visible in his dimension might mean something, but I doubt all the full moons we see are connected xD that would be too over-thinking as well.