What has many keys but can’t open a single lock?

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

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 brings you down but never up?

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.
Now all your friends have one apple each, yet there is an apple remaining in the basket.
How?

I look at you, you look at me I raise my right, you raise your left. What am I?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

I’m tall when I’m young, and I’m short when I’m old. What am I?

What seven-letter word has hundreds of letters in it?

Can it be possible to build a house that has all its four walls facing towards the South?