I don't want to buy duplicate cards but the cards I bought are added into the deck immediately so I can't check which one I've bought unless play the game with someone.

Usually they don't get added to your dec immediately(bug). No you can't buy duplicate cards. If you can it won't let you use them. Also, if you do run into the bug for Caravan Cards not adding to your deck there is a work around. You have to find a mojave express box place them in there, and hit the take all button. Don't send it or you will have to travel to the town you sent it too. Hope this helps. Also if you have a hard time finding your Caravan cards they are under all items not Misc. I think that is a bug as well seeing as since they should be added to your deck immediately.

Actually I'm playing the PC version so the caravan card bug isn't much trouble as it is solved by a mod.
What concerns me is that buying the same card from one set will make the deck cumbersome as they can't be used but still show up in the deck.
Is there a way to prevent buying the same card of set from happening as I don't want to mark down which card I've bought and which haven't.