What has one letter and starts with an E?

I get hot but I never sweat,
I cook food but I am not a chef,
I have a door but you can't enter me,
I have a light but I am not a lamp.
Who am I?

I have a big mouth and I am also quite loud! I am NOT a gossip but I do get involved with everyone's dirty business.

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

Samuel was out for a walk when it started to rain. He did not have an umbrella and he wasn't wearing a hat. His clothes were soaked, yet not a single hair on his head got wet. How could this happen?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

What demands an answer, but asks no questions

During which month do people sleep the least?

How can you write nineteen in a manner that if we take out one, it becomes twenty?

What month of the year has 28 days?