I am new to Illustrator and I am editing artwork which seems that it is drawn by paths.
My problem is I am unable to fill the part which is selected in the below image:
How I can fill the shape with a color?
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It looks like it isn't actually a stroke, but rather it is it's own shape (you can see on the left that it shows filled with black)
What you would need to do, is merge it with the shape. Use the shape builder to join it.
Select all, then just drag areas to merge.
You can now fill with any color you want.
There are many places where you can choose colors in Illustrator, my two favorite are:
Swatches (Window → Swatches) and Color (Window → Color or F6)