After you unpacked your cards you can go to the same hotbar option and on the right you will find all the cards you're currently using for those card battles I mentioned earlier, then you can choose to switch them for the cards on the left :Thank you, I know the initial part, but then what to do with it?
After you're done with all that you can go fight others if you want.
Also the purple cosmo dude in the park is used to sell your cards (only if you have more than 1) and to eventually buy other packs (they cost 9 points each). You get the points by selling your cards.