"Feels like" isn't one formula — it's two, switched automatically depending on conditions. Below about 10°C with meaningful wind, the wind chill formula estimates how much faster moving air strips heat from exposed skin. Above about 27°C, the heat index formula estimates how humidity blocks sweat from evaporating, the body's main cooling mechanism. In between, wind and humidity have only a minor effect, and "feels like" is just the air temperature.
0°C with a 24 km/h wind feels like about −6°C — noticeably colder than the thermometer, though still short of serious frostbite risk over a short exposure. 32°C at 70% humidity feels like roughly 40°C, squarely in the NWS "Danger" heat category, even though the thermometer reading alone looks merely hot.
NWS testing found humidity changed the result by less than a degree, so the official 2001 formula leaves it out entirely to keep the calculation simple and reliable — wind chill is driven almost entirely by temperature and wind speed.
No. Wind chill can never cool human skin below the actual air temperature — it only describes how much faster heat is lost. If the air temperature itself is above 0°C, frostbite from cold exposure alone isn't possible, whatever the wind chill number says.
The core Rothfusz regression is a statistical fit, not a physical law, and it drifts at the extremes — the NWS adds small correction terms for very low humidity (which lowers the index, since sweat evaporates efficiently) and very high humidity at moderate heat (which raises it further).
For heat index, yes — NWS notes full sun exposure can add up to 15°F (8°C) to the effective heat index versus the shaded value this calculator produces, since the chart itself assumes shade and light wind.