We mostly use classical C strings, but the memory management around them
can get confusing and error prone. Let's use std::string for the cases
where we need to return a newly allocated string.

This allows us to separate accidentally unused, from explicitly unused
parameters, which allows us to turn on such checks in the compiler.

The generally recommended way is to include it from source files, not
headers. We had a mix of both. Let's try to be consistent and follow the
recommended way.

Some code points are reserved for the UTF-16 coding itself and must not
appear as input data to the algorithm.

Signed bug prevented anything not ASCII from being coded correctly.

Everything outside of BMP was handled incorrectly and was coded as
completely different code points.

This would mess up most conversions from UTF-8 as the caller wouldn't
know how far to step to get to the next valid character, resulting in
markers for invalid data to be injected here and there.

Also add some unit tests to avoid this reoccurring.