It depends on the company and if they have a warranty on the tv. If you purchased a warranty for the tv, you can check with the company to see if the damage is covered by the warranty.
No. A damaged plasma usually results in the actual PDP unit being damaged and any argon gas being released, this is the largest and most expensive part, not easily fixed.
Most companies will warranty these items for one year and the store that you bought it will take it back within 90 days. After 90 days, call the manufacturer.