Clean-Up examples directory

The current examples directory is very messy, with old and new examples.
We need to create a few examples that are easy to run and understand with clear intentions.

Additionally we would like to add a README file explaining what are the requirements for adding an examples directory.

Start by inspecting the existing examples directory and running the current examples to understand which are old, unclear, or difficult to use. Define a small, coherent set of easy-to-run examples, then add a README in the examples directory that explains requirements for adding future examples; done means the examples are understandable and the README documents those requirements.

Written by the indexing model from the issue text.