About the skill points: if you are a male worrior then it is normal that the sword and augment damage skill have lvl2 without a point spent.
For the healing gem: use the pool to the lowerright of the map. East of Georges house IIRC.
For lockpicking: This is possible. The lvl could be too low. But the ones you n eed now have a key or are low lockpicking. I think you are referring to the chest in Mordaneus house? I think it need lvl3 lockpicking. Just return later on that one.
Remeber that you can "get" some skillpoints of this through quests
