How do I get my esior's fields to appear again if I'm beginner....I'm not sure if I in the game far enough that I can pick it as an option.

And is the new fable pet, Ryori capturable with the standard snare trap? Or do I need a different trap?

Esior's Fields are not accessible again after you beat that part of the game until the festival zone is opened (which should be later today). Also, I believe the Fabled pet, Ryori, will be able to be captured the same way any other pet, it will be able to be captured with the snare traps that meet the rarity of the encountered pet, ie. common(white stars), uncommon(green stars), rare(blue stars), or epic(purple stars).

Are you asking about the "Holiday Zone?" If so, it's not available yet. Esior's fields, like Edi said, is technically an area you can only access right at the start of the game, however during festivals it becomes available to everyone as the event zone.