Regards checking for eggs: leave the mop in the aquarium for a week and then change it with another one. If you don't have experience with collecting the eggs by hand, I would check in the mop for any eggs but will not touch them unless you have a nice number of hatched fry. I would transfer the mop into another container for hatching. Use the same water ofcourse.
Then when you are satisfied that you have some fry, try picking up the eggs and put them in a small hatching container (could be a margarine container). Make sure you pick them up with wet hands, they're a bit delicate as one can imagine. But with practice you'll get use to it.
Let us know if you find any eggs, but from the behaviour you described, it seems they started breeding.