1. Usually one would say "The water cleared after the mud had settled". For me, this seems ambiguous. Perhaps it means that the water became clear (i.e. pure and transparent, not muddy), or perhaps it means that the water flowed away.
2. Yes.
3. Yes, they can both mean that (both phrases could also be interpreted in other ways).
This is very ambiguous. The water cleared means it became less murky, particles have settled down and seperated. After the water cleared is also a euphemism (an expression that means once things have settled, we can see it more clearly, the aftermath - a similar idiom is "once the air has settled).
Additionally it can mean after the water has gone away. "We had a flood, but the wate