What is the name of the drawing having free hand shapes of animals, birds, flowers combined together to form a pattern/story?
I would classify these images as line art.

With line art you will see clear lines defining forms and shapes, and sometimes where color and light would be, but the color and shading won't be there.

Definition is enhanced in compositions such as the ones posted by varying the line weight and and stroke. The thicker lines make parts stand out, and also help define depth.

Since the line weights vary in these examples, they may have been drawn using some type of ink (presuming they weren't digitally produced). Pen and marker tips allow for more variation in line weight than a typical pencil, although it's possible to sharpen a pencil in such away to allow for more variation.

Line art itself isn't going to be subject to less rules of composition than other 2D visual arts. An understanding of composition in general is going to be helpful, although outside the scope of this answer. 

However, certain techniques or media may be more helpful to practice with, if the end goal is this type of art: Drawing in general, inking or other practice to help with line weights, and making clean lines.

Making clean lines can be achieved by learning how to use such tools as French curves, templates, stencils and compasses: 

Here's an example of some French curves: