If you really wanted to, you could try giving the eggs some brackish water to hatch, later slowly dilute the snails to freshwater. Never tried it but I haven’t seen any eggs to do so.
Regarding who laid the eggs, unfortunately only direct observation (I.e, seeing the snail doing it) is the only way. And then, you will know that snail’s gender forever.
Unlike rams horns and pond snails which are simultaneous hermaphrodites (both genders in each snail), nerites are separate genders (either male or female). In that regard they are like apple and mystery snails.