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Leaving the shoot on will make it lop sided. It would be best to cut it off and plant it. If sap gets on you, it needs to be washed off right away because it will look like a burn.

Yes, they do flower.

I got my coral cactus as a gift and it is potted in a painted clay pot without a hole for drainage. The highest has small white stones that look to be glued at the side of the plant coming out of the middle. I do not think there's any soil of any style in this pot because I watered it then tipped the pot and poured out the water and the water ran clear. I've never seen a plant planted like this earlier than. Must I repot my coral cactus in a pot with drainage and in a cactus medium? Thanks in advance.