This whole article is incomplete. Please feel free to edit this whole article to add missing information and complete it. Reason: A whole lot of stuff based on my serious lack of knowledge of both Gen V and the anime. Feel free to lend a hand :)
A Munna used in Fennel's research at the Dreamyard is encountered early in the player's quest. After obtaining the Trio Badge, Fennel asks them to fetch some Dream Mist for her. However, Team Plasma, also wish to obtain Dream Mist, and are abusing the Munna in order to acheive that end. After they have been defeated and scared away by a wild Musharna, the player obtains the Dream Mist and Munna is saved.
Fennel is also shown to be the owner of another Munna seen in the Pokémon Dream World. This Munna, nicknamed ドリームDream in the Japanese version of the site, is seen when the player uses the demo version of the Dream World. Having no Pokémon of their own to send to the Dream World, they are instead accompanied by Dream. She has a Docile nature, was caught in a Premier Ball, and is at level 10.
In the anime
Fennel and Munna in the anime
In the anime, Fennel's Munna helps her with her research on the Dreamyard and Musharna. It first appeared in Dreams by the Yard Full! when Team Rocket had awakened Musharna, when Fennel noticed its eyes were suddenly glowing pink. It was then seen with Fennel helping Iris's Axew wake up by sucking off the Dream Mist caused by Musharna and revealing Axew's dreams. Later Fennel, Munna, officer Jenny, Iris, and Iris's to-be travel companions rushed to the Dreamyard, where they found Team Rocket had caused all the problems. Munna helped call for Musharna which appeared.
Suddenly Team Rocket captured Musharna, however Munna used its Psychic to cripple the machine, giving Pikachu a chance to destroy it with Volt Tackle and free Musharna.
Munna reappeared with Fennel and Musharna in BW039 where the three of them were studying an Archeops.
