1) Pets/companions that were native to Ensō would have gone wild on the mainland after a character is dropped. They can be reclaimed without any item request necessary - one simply has to find them, and potentially re-domesticate them.

2) In the case of a wyvern, it would depend on what sorts of abilities and intelligence it has. We'd want to ensure that the wyvern is not, after all, a potentially appable character! It may have its size reduced, and it would undergo some nerfs if it's flight-capable, to level the playing field for explorations. Requesting such a mount might take something like three to four stories, depending on what kind of complexity we're talking here, and whether or not riding gear is required.