PRO Magic the Gathering MTG Deck Bag Travel Case - Card Protector Bag with Padded Shoulder Strap , Customizable Interior , Weather Resistant - Fits Loose Cards and Boxes - Red

Q: Does it come with the deck boxes an white storage box as shown on images?

No. It only comes with the case itself.

Q: Will this work for Pokémon cards? If so, will it work with Pokémon deck boxes and sleeved cards?

Yes it will work with any standard sized cards and card boxes. Right now my son has MTG, as well as Pokémon cards and three deck boxes (one large leather one and two cardboard). His loose cards are mostly sleeved in the sleeves that just fit the cards, but a few special ones are larger, and stick up about the height of the deck boxes.