Game starts with 3 "heroes" each with their own deck pool. In each fight as long as each hero is alive you will pick a card from their pool to your hand to play. If one hero goes down, that characters pool is out. You can unlock 3 more heroes as far as i know.
While every character has their own pool that consists of attack, defense, passive/active buff&debuff and what i like to call "special" cards, they dont differ that much from each character meaningfully enough - just a bit strategy changeup and otherwise you can keep on playing each run similarly to complete them.
You gain trinkets, potions and equipment which give nice diversity for overall aspect of the game, but unfortunately especially equipment give so little bonus that it feels a bit unnecessary to use your time trying to min-max stats that way. On the other hand i felt trinkets are well diversed to make rather big impact on your runs if you end up missing good ones for your strategy.
Equipment, character level ups (gaining access to new cards) and trinket of your choice will be with you between new runs, card decks however tend to start from the "starter pool" without ability to keep some cards from last run. So basic thing going on here. If you got the recipe and ingredients (accuired from past runs) you can also brew potions for your new run to help you out (max 4 potions at the time).
Also yes, there is a way to remove a card from your deck and it is not even that hidden feature - you just need to know who can help you with it; it is not something you can do in every step, that would be odd choice.
I dont find the game ugly, too difficult or bizarre. It is nothing groundbreaking, but neither it is anything awful enough to make you not purchase the game (especially on discount). You will get your fun out of the game for couple of days if nothing else.