Can you encounter the moon nymph encounter again if you lose them to a quest interaction, or is there somewhere I can hire a new one?
Also what is needed for the mini quest for the recipes for the dragon forms and fox romancers?
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The moon nymph is a repeating random event, so yes, you'll have a chance to recruit a new one later. In the future there will be fixed point of interest that'll allow you to recruit one or two, similar to the raccoon bandit camp, wolf den, etc.
All you need is Lavaheart gems to learn the recipe for dragon potions, found in the same location as the quest. Fox romancers I don't remember off the top of my head but I think you have to pass a flirtation check or, failing that, gift them some wine.
The gems are intentionally hard to find as the dragon potions are meant to be hard to craft. Dragons have few penalties that matter much by that point in the game where the party will likely have multiple tens of thousands of gold.
Do you the player or a companion invested in Foraging to increase the odds?