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It depends where you live and which species of 'Dwarf water lily' you have. Two looking alike 'dwarfs' are interchanged in pet shops but they are different. Do you have Nymphae mexicana or Nymphae aquatica ? Hopefully, the seller identified the plant. Here is a reliable link that might be useful: https://www.fnps.org/plants
I apologize for not answering your first question. These plants are semi-hardy.
Common Yellow Waterlily or Banana Waterlily (Nymphaea mexicana) is a hardy water lily. It stays relatively small 2-4 feet wide. It is considered hardy to at least USDA Zone 6 (-10º F/-23º C), perhaps more depending on locality and shelter.
White Floating Hearts (Nymphoides aquatica) is not a waterlily but the leaves somewhat resemble one. The flowers are quite different. It is in an unrelated family: the Bog-bean Family (Menyanthaceae). It is considered hardy to at least USDA Zone 8 (10º F/-12º C).
Both plants are native to parts of the southeastern United States, as well as Mexico.