Fix non-runnable code examples (undefined variables, syntax errors)

[lacatoire]

This fixes a batch of code examples that cannot run as written: undefined
variables (missing $ sigil or a variable name that does not match the one
declared), a few syntax errors (a missing ;, a stray ., a = instead of
=>, an unterminated string), a Cyrillic homoglyph in a type hint, and a
couple of new calls referencing the wrong class name.

Each change only touches the example so it parses and runs as intended.

Part of #14.