Stipe - if you have that many snails, they'll probably eat it pretty quickly so you won't have to worry about how long to leave it in for. They are nocturnal, so just drop a piece of food into the tank when you go to bed, and if it's still there in the morning, take it out.
Pest snails stay very small their entire lives so yes, it's possible that these could be the snails that are laying the eggs.
If your snails are in fact Physids, then they will be hermaphrodites. They of course prefer to reproduce with another snail, but that is why you will have to get all of them out of the tank. Sorry to be the bearer of bad news!