"The Blue Period of Picasso is the period between 1900 and 1904, when he painted essentially monochromatic paintings in shades of blue and blue-green, only occasionally warmed by other colors." Some examples of paintings that he made during this period include: The Blue Room, La Vie, and The Actor.
Picasso made sad paintings of war during his blue period. The color blue reminds you of sad and dark times. When he was in his blue period there was a war going on so he painted about that.
Unless they use a good finish and keep it under certain temperature and humidity the wood may rot or deteriorate over time. If it is in the public within reach of people it may also chip and break apart.