In order to remove the sword from its stone, your Hero must have upgraded physique, health, and toughness. Specifically, after your first attempt to remove the sword, you must upgrade physique by five, health by two, and toughness by three.
The 'Sword' in Question can be found at the Temple of Avo in Witchwood. And if planned out right, can be gained almost immediately apon entry. The best way to achieve this, is to spend 0 points on the 'Physical' section until you arrive at Witchwood. Which ofcourse makes the game a lot harder, but well worth the challenge.
When you arrive at the Temple of Avo in Witchwood, try to pull the Sword from the stone. You will fail. But the people around you will remark about different abilities that you need. 'He was a lot tougher then that' Means that you must upgrade your Toughness. 'I think you need to exercise more' means you must upgrade your health. 'I think you need to work on your physique' means exactly that, to upgrade your physique.
To Summarize:
Physique - You need some more 'fresh air and exercise'.
Health - You better come back when you're more fit.
Toughness - You're not tough enough.
As for the shooting contest, this is unlocked after the 'Siege of Knothole Glade' mission and is incredibly easy if you have a decent bow (speed upgraded.) or the Bow of Skorn (found by sacrificing a Mercenary at 4am at the Temple of Skorn; found at the Witchwood Camp.)