If you want to hibernate your turtles, refer to one of the books listed below. These are not clean-cut rules, and not all work for all turtles, but using a combination of them, will usually help you determine the gender of your turtle. Males often have fatter, bigger tails than females. Females have it closer to the shell. Females have a flat or convex plastron - so there is more space for eggs.
Male sliders grow long claws on their front legs.
This is an advanced feature and not covered here. If you keep a pair of turtles, and their are eggs in the water, you have several options. Most likely those eggs are already dead. Or take the eggs out immediately and try to incubate them. If you want to encourage your female to lay more eggs, provide a land area with sand or dirt for her to lay her eggs.