Those are indeed supernatural claims. They invoke a supernatural explanation for some aspect of the universe.
In the case of a young earth, a person is invoking God to explain away the amazingly precise relations between different independent dating methods that indicate an old earth.
In the case of a global flood, a person is invoking God to explain away the evidence that a global flood did not happen.
In the case of lightning caused by a deity, the use of a deity in the explanation makes it inherently supernatural. This also applies to the first two cases.
In the case of the evil spirits hypothesis of disease, we are invoking a supernatual entity to explain an aspect of biological life.
It is not the fact that these attempt to explain the universe. It is the fact that they do so
using or involving a supernatural entity which makes them supernatural.
So yes, these
are supernatural claims. And yes, they are also wrong. But those two properties are not related.