How to deal with the stains on a cement-based leveling floor?
I don't see anything out of the ordinary. Remove the small burrs, vacuum it up, glue it on. So there are cement smears in it, so what? It's always been that way. It has a coating on it. Or is it not cured?
I don't see anything special there either.
These are typical drying spots that you can't prevent. but they are only surface spots. once the floor is sanded, they will disappear. re-pouring won't do any good, because you will have the same thing again ...