https://en.wikipedia.org/wiki/Dew_point
https://en.wikipedia.org/wiki/Humidity#Relative_humidity
In the US, the 100th meridian is a popular demarcation for the half of the country that experiences high humidity versus the other half that experiences low humidity. It is why 100F in Phoenix, Arizona is much more tolerable than 100F in Atlanta, Georgia.
No, usually not, because they're usually just simple toys combining a heat index and wind chill scale.
There _is_ an official metric used for estimating heat stress that accounts for cloud cover - the Wet-bulb Globe Temperature (e.g. https://www.weather.gov/tsa/wbgt). This is what is used, for instance, in literature analyzing the impact that future climate change might have on heat stress and mortality risk during heat waves. It's also used by some professional sports programs to monitor risk for crowds and athletes, as well as commonly used by OSHA and other regulatory agencies looking at worker exposure to heat hazards.
In cold weather (wind chill), wind strips away the thin warm layer of air next to your skin, so you lose heat faster. Hence, "feels colder".
In hot weather (heat index), humidity slows sweat evaporation, so your body can't cool itself as effectively. Hence, "feels hotter".
So it's a lot more useful for decision-making (like what to wear, weather it is safe to run/hike, how much water you need, etc.) than the plain temperature.