It wouldn't hurt the betta, a lot of them actually prefer darker water. As for the soil, I would use a fine net to get anything at the top. The rest will settle on its own and you can try and re-cap it then. Though if you have a temporary home, use it.
Agreed. In the future, put a plate down on the sand and pour the water directly onto the plate. This will prevent the sand from stirring up again. Also, how thick is the sand cap? It might be you need to use just a little more sand to keep the dirt down.
Uughhghghhh That happened to me, too. I was never really able to fix it. And I was an idiot because I didn't sift the soil so there's pieces of bark all over the bottom of my tank so I wasn't able to re-cap it.