You can split, if you have a good flow or are willing to feed. How good are you at finding the eggs or just hatched larvae?
Are you planning on buying a queen to add to the split or are you planning on letting them raise their own? How much of your ten frame is brood?
I would take two brood frames with the queen to the split. If you have drawn comb it will give the queen in nuc something lay on right away. Many do keep splits in the same yard. You will need to watch for robbing. Some leave splits in the same yard without any problems, but I have had splits get robbed in my own yard. Put a minimum or one frame of honey/pollen in the nuc.
They can grow fast, so be prepared to add a second nuc box on top. Hope that I answered all of your questions. Make sure that you have the eggs/newly hatched larvae in the hive that is left without your queen.
Yes you can split the hive and it's fine to keep it in the same yard. Just divide it in half. If you can find the queen, great. If not, make sure that both halves have at least one frame with eggs or very small larvae on it. In a few days check to see that they have drawn queen cells in the hive without the queen (or if you hadn't found the queen, one hive should have cells and not the other). If you see cells, wait a month and you should have a new laying queen and be able to see uncapped brood.
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