Update the examples/ README and associated fixes. (#9090)

This yak shave went as follows:

Fix https://github.com/flutter/flutter/issues/8795 by adding stocks to
the examples README.

Notice the layers entry in that README isn't quite right either.
Update that.

Check the layers/README file is worth pointing at.

Update the layers/README.

Let's run some of the layer tests to see if they still work.

Oops, need to update them to gradle.

Ok let's try running them again.

Oops, sector is broken.

Add a test for sector.

Fix sector. Find you need to add an assert to a const constructor.

Notice we need to turn const asserts on for the analyzer.

Notice the analysis_options files are out of sync with each other and
with the full list of lints.

Turn on the lints that should be on.

Fix the bugs that finds.