At the moment, card draw is random but weighted. The card pool is fixed since there's very little content.
Housing cards are timed, yes. While nothing stops you from doing that, it shouldn't be possible in the future with proper balancing. They will come in different shapes, take significant space and require rarer biomes.
I just joined another jam that ends in a week, after that I'll focus on 1 or 2 big batches of new cards before adding proper deckbuilding :) Still not sure if I will make the game a Roguelite or level-based.
I'll have to change the card layout and size sometime to allow for more & bigger text. Biggest roadblock atm is the lack of space, so I'll have to implement fancy animations for that.
