Why can I not clear these two cards?

Either they do not add to 13, or one of them is covered. A card is only playable when both cards resting on it have gone.

Do Kings need a partner?

No. A King is worth 13 by itself, so a single tap clears it.

Is every Pyramid deal winnable?

Far from it. Pyramid has the lowest win rate of any mainstream solitaire — figures near 2% are commonly quoted for a single pass through the stock, and many deals are impossible from the moment they are dealt.

Can I pair two cards from the stock?

Only the turned-up card is available, so no — you can pair it with a card on the pyramid, but not with another stock card.

How long does a game take?

About 5 minutes. Pyramid is quick, which is just as well given how often it is unwinnable.

How to Play Pyramid Solitaire — Rules Explained

How to Play Pyramid SolitaireLearn Pyramid Solitaire: pair cards that add to 13, which cards you are allowed to touch, and why counting what has already gone decides the game.