This might sound like a really stupid question but is there a way to color the area i marked with red color? I tried enclosing the mouth area with the red line using pen tool but obviously it's not working. Is it possible or do i need to trace the whole mouth area?
Draw a closed shape that will fill the space you want in the gator's mouth. Set the Fill to the red color you want and then choose Object> Arrange> Send To Back which moves it under the gator shape in the Layers Panel.
EDIT- Additional information- It seems you were trying to "paint in" the red color for inside the gator's mouth. With Vector artwork, for the most part, you need to think not in terms of painting or coloring areas but more in terms of stacking shapes- more similar to cutting out pieces of colored paper and then stacking them together.