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It is probably powdery mildew. This article will help:
https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm

You can treat it with either a chemical fungicide or neem oil. Both should be available at any store that sells gardening supplies.

This article should help you with that: https://www.gardeningknowhow.com/ornamental/trees/palms-trees/propagate-palm-pups.htm

You do not need to do anything for the mother plant. The wound will harden off on the mother the same as it does on the pup. If you try to cover the wound, you can actually create an environment where disease and fungus can grow.

It would be helpful to do so. You can get some other tips here: https://www.gardeningknowhow.com/plant-problems/environmental/protect-plants-in-freeze.htm

They can survive short bursts of cold, but not for very long. I would cover the plants if possible. This article can help you with protecting your plants during an unexpected freeze: https://www.gardeningknowhow.com/plant-problems/environmental/protect-plants-in-freeze.htm

This article may help you with that: https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm