Guess getting monster cards is way less complicated than they made it out to be since it sounds like he's already gotten a few in the short time skip and either sold them or hasn't used them because they were male/gross monsters.
the drop rate depends on the rarity of the monster, getting a drop from a low rarity card is much easier, that plus renka has the ability to increase luck, and another detail is that the frequency of exploration of the MC is really high, he goes every day, when the common people visit once or twice a week.
is there a max of cards he can use or he can like have a army?
About the card slots, they depend on the dungeon lvl from 2 cards up to 12, with some details, there are certain cards that work in a set of 2 or 3 and when they are together only use 1 slot, there are also cards with the ability to summon minions, the card limit is per person, and can be solved by acting in groups.