Pokémon Mystery Dungeon: Gates to Infinity
In this installment of Mystery Dungeon, Ho-Oh can be encountered as a Shiny Pokémon. Should this happen, it will use different moves and overally be more powerful.
It's met on a job request and is non-recruitable. Since PMD: Gates hasn't been released for that long yet, it's not clear if shiny Pokemon will appear. However, I haven't seen any reports of shinies in Gates, so I would assume Ho-Oh is a one-off like Celebi in Explorers of Time/ Darkness.
Bulbapedia - Shiny Pokemon
After the player returns to Pokémon Paradise and completes one dungeon, both Pokémon and recruited Pokémon may now evolve if the player chooses to evolve them inside of dungeons.
So as you level up in a dungeon, as long as you're at the correct level, you should evolve.
Bulbapedia - PMD Gates to Infinity