During which month do people sleep the least?

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.

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

There was once a troop of 5 elves. The 5 elves were very dedicated on finding the magical treasure of 1000 coins. However, being elves, they were super geniuses, very greedy and they did not hesitate in taking lives of other elves. The 5 elves were named Aye, Bee, Cee, Dee and Ee, ranked from high to low respectively, from Aye to Ee. One fine day, their efforts brought results and they found 1000 coins. Now they had to split it in between them as per their ranks. The lowest ranked elf has to make the proposal. If the proposal is accepted by majority, it is agreed, or the suggesting elf is killed.

What proposal should elf Ee make ?

Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

Can you count the number of quadrilaterals in the picture below?

Why is Saturday stronger than Monday?

A game is being played where eight players can last for thirty-five minutes. Six substitutes alternate with each player in this game. Thus, all players are on the pitch for the same amount of time including the substitutes.

For how long is each player on the pitch?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

How many letters are in the alphabet?