What are some accessories and costumes you can put on your pet? And how do you put them on your pets?

I'm... not entirely sure what this has to do with increasing Mana, but anyhow:

The Costume thing that is with the relic/armour/accessory squares was intended to be exactly that, purely a costume for aesthetic purposes.
However, so far as I am aware, the only one ever released was the [Griffi Costume: Father Winter's Helper]

and the idea was effectively scrapped for a few reasons including time going more towards the pet revamps and lack of overall interest.

Accessories, on the other hand, are obtained and equipped in exactly the same manner that the relic and armour are. They have the same function as armour, additional stat boosting.
They do boost mana, but in relation to their rarity, rather than their level. Unommon gives 2, rare gives 4, epic gives 6, legendary give 8, and mystical give 10 (meaning the maximum boost in mana you can get from accessories is 20 points with two mystical pieces of equipment)

I was told accessories and costumes increased mana. I don't know.
But thank you!

Just letting you guys know: there were several other costumes released. They are all available in the diamond shop under the 'pet costumes' tab. There are:

Father Winter: Aurleon, Draeyl, Griffi, Qitari, Sylvorpa, Vulnyx, and Zolnixi
Forest Guardian: Morkko
Valentine Masquerade: Luffox

Just thought I'd let you know ^.^