Yes you can order a new screen but this is usually very expensive. Replacement screens can sometimes cost close the the price of a new flat screen, sometimes even more.
Depends on your use and your opinions. LCD images are more easily "washed out" by light sources in the room but have less glare (no glass screen). LCD's have a much longer life span that Plasma...
A properly operating CD player will not damage a CD because there is no physical contact with the disc except in the center, where no music is stored, however a defective player can damage the disc...