Where did knights keep their swords?

If they were station at a castle- it would be in the castle armory or in their barracks, and if they were not and at home they would keep it some place in their manor house.

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What would a knight carry?

Weapons. Besides a sword and a lance (for knocking an enemy knight off his horse or spearing him), knights might carry a mace(left) or a flail(right). As time went on, knights began to wear more and more plate armour (made out of sheets of metal) over their mail. Subsequently, how many weapons would a knight carry? Anywhere from one to half a dozen or so. A mounted knight riding into battle would typically carry a lance, a sword, a dagger, and an impact weapon like a mace, warhammer, or axe. If fighting on foot, he would have a poleaxe or similar weapon. He had spares for most of his weapons back at camp, especially extra lances.

Did knights use battle axes?

Well, according to an article, the weapons of an English medieval knight in combat included the long sword, wooden lance with an iron tip, metal-headed mace, battle-axe, and dagger. So, yes, knights do use battle-axes, at least for the English medieval knights.