As in dried creek bed, are you referring to the light brown shaded area on the very left?
Yes.
If so then no. There is not a way to "flood" that area.
Oh :(. That's a shame because it would be nice to have a stream there, especially since there's a waterfall flowing into the lagoon. I know it's a magic lagoon, but in real life it would have overflowed and swamped the village by now.
As for the chest, it seems only to be there so the villagers have something to admire.
Again, it would be nice if the villagers could do something with it - maybe put it at the feet of the idol or in the temple or something similar - rather than just leave it on the beach.