"Wish you peace and well" sounds odd. Firstly, it's typically said 'I/We wish you ...'. Secondly, wishing a noun and an adverb (peace and well) sounds unnatural. Peace and good health?

Claire is right. You can't say that you wish someone an adverb. For example, you can't say "I wish you happy." You can say "I wish you happiness." You can't say "I wish you good," but you can say "I wish you good luck" or "I wish you a good trip." So you need to replace the word "well" with a noun. Claire's suggestion of "good health" sounds good. If you're translating 祝你端午節安康, I would say "I wish you peace and good health for the Dragon Boat Festival!"

"Wish you peace and well on the Dragon Boat festival" The first one that uses "the" is correct

Hello friend I'm new here and I want to learn Chinese I'll be glad if you can teach me Chinese language and in return I'll teach you English