You can set the day they are laid no problem. You don't want to set eggs daily because they will hatch daily and that is a lot to keep up with.
I don't know of any other type of Barnivelders but double laced (blue and reg) BUT they are not a breed I follow. Seems like there was a another laced type but i can't remember what it was.
That dot is a sure fire test of fertility.
There are also silver laced barnevelders - they are double laced. If my memory serves me correct they lay a white egg, not a brown egg like the blue/regular laced. Well, at least the ones brought into the US do.