I keep opening an Idol that says it contains a collector card, it shows me the card and then i click ok and it goes away. I dont know what is happening with them.
The disappearance is the intended purpose. Collector cards work in such a way that once you collect all five, then you will be granted the corresponding achievement, along with $5000. You can view which you have collected so far by heading to Achievements > Achievements > Items > Collector Cards > "+" sign on any listed achievement.