I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

What number divided by 4 is the same as that number minus 4?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

What does man love more than life, and hate more than death or mortal strife; that which satisfied men want; the poor have, and the rich require; the miser spends, the spendthrift saves, and all men carry to their graves?

The below given figure comprises of a pattern through which you can determine the missing letter. Can you push your mind to find the pattern and add the missing letter?

If eleven plus two equals one, what does nine plus five equal?

Can you identify the Oscar-winning movie from the rebus below?

A pregnant woman is preparing to name her seventh child. Her children's names so far are Dominique, Regis, Michelle, Fawn, Sophie, and Lara. What will she name her next child -- Jessica, Katie, Abby or Tilly?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?