No. Carbonic acid is inorganic.
yes - carbonic acid is a week acid. eg Ordinary soda- which is carbon di oxide dissolved in water.This is unstable.
Yes, carbonic acid is dibasic acid because it gives two H+ions on IONIZATION hence it also gives two types of salts carbonates and bicarbonates.
The definition of an acid is commonly known as a substance which can produce hydrogen ions (Hydronium ions to be more precise) in solution. However, the currently more 'correct definition' of an acid...
It's an organic acid.