When they've finished flowering, stop watering them and keep them in a cool place to dry out. Pot the corms up in the autumn in fresh compost, with the corm just showing, and resume watering. Don't water the top of the corm, though - it'll rot.

Someone else can probably help with the propagating bit! I hope this info. helps you.

All Cyclamen are propagated from seed. You can cut up really big C. hederifolium corms as long as there is a growing point on each section, but it is rarely done.
You need to see if when the flowers are finished they develop pods on the end of the stalks. If they do you need to wait until the pod is ripe. Then it will begin to split. When this happens, then surface sow the seeds as they do better not covered with compost, but you can put fine grit over them if you wish. They take about 16 months from sopwing to flowering in ideal conditions.