I am an engineer and concrete specialist. The "dust" can contain many chemicals: one such chemical can be coal ash. Which may or may not be harmful to our health. Studies are not certain. If it is sealed, as mentioned, this will prevent particles from separating and then becoming dust. Depending on how thick your ceiling is, the concrete could be drawing moisture out of the surrounding air; therefore making your breathing air drier. But probably not dry enough to cause any problems. Depending on where you live in the world and on when the concrete was installed, there could be asbestos material in the concrete. But, as long as it is contained (sealed) the asbestos cannot enter the air.
Generally, indoor cured concrete does not put off dust. However, if surfaced with a grinder or if the concrete is breaking apart, there will be dust particles omitted into the air. Normal indoor use and contact with modern stable/stationary concrete in the USA is not harmful.
No. The only possible hazard is from dust. This is unlikely in a form-finished floor. The forms generally provide a smooth surface. If there is roughness there are numerous sealants available designed for concrete that will completely solve that problem.