When you go to your badge page it will say it above the ones that you still need cards to get.
Remember you will only get half the cards you need from the drops the rest you need to get yourself.

nope works the other way
more games you have on at the same time the longer it gets for a drop

I think it has something to do with the new refund policy they brought out last year.

The Steam refund offer, within two weeks of purchase and with less than two hours of playtime, applies to games and software applications on the Steam store.

So after the 2 weeks I think they go back to the normal drop rate.

Not all games have cards so out of all the games you have looks like only those ones have cards to drop

ObEyZ^ you can only get the cards if you have games that drop them
you have 3 games

Counter-Strike: Global Offensive

Dragon Nest Europe

Games of Glory

so your not going to get other games cards as you don't own them