Ny benefit to having foil cards

The opponents you are facing are special Encounters in the campaign. When you did your first encounter, there should have been a popup telling you that Encounters are specifically designed this way in order to help you improve your skill at facing specific strategies. These matches are specifically labeled with Encounter in front of the name of the match, like Encounter: Disturbing the Nest and Encounter: Face of the Ghoulcaller.

Encounters will always play out the exact same way. For example, during the Encounter Stampede!, the AI will always play a Willow Elf on Turn 1, followed by a Runeclaw Bear on Turn 2, and so on.

Encounters also, as you have noted, have decks that are exempt from the limit of 4 of the same type of card.

The Planeswalkers you face in the campaign and other opponents, like Odric, have decks that are subject to the 4 card rule. Note that the game with them will also be different each time you play, in contrast to the Encounters, which always play with the same order, use the same strategies and same cards.

No, they're not. Wizards of the Coast has the full decklist on their site, and there are no planeswalkers in any of them.

It's pretty confusing as to why they show them in the character intros: my guess is that they're intended to be minor advertisements for the physical card game or Magic Online.