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The Jack of Hearts faces right, as seen from the card's perspective.
Just one. After that you no longer have a card deck.
In a full deck of 52 cards your chances are one in thirteen. The same goes for every other card as well not just jacks.
There is one Jack of Spades in a 52-card deck.
As there are 2 black queens in a deck, the chances of pulling one from a 52 card deck is 2/52 (or 1/26).