Where are you?
Do fellow beekeepers run two brood boxes in your locality? If they do you should be running them similarly till you get the flow frames on.
If the brood frames are not drawn it might be too early for your super.
If you are seeing cells with eggs then your queen should be there.
These queen cells, post a picture.
Are they queen cups or queen cells? Is there anything in them?
Yes best not destroyed till you know more
Drones, yes leave.
Have a look here
http://forum.honeyflow.com/t/there-are-queen-cells-in-my-hive/5272