What is both possible and impossible at the same time?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

I organized a small get together at my home.
In the party , i have a barrel with some whiskey in it.

Suddenly Guest 1 say 'I bet this barrel of whiskey is more than half full'.
'No, it's less than half full' Guest 2 replied.

I don't have any measuring instrument and without removing whiskey from it , how can i determine which of the guest is right ?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?

If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

What has hands, but can’t clap?

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?