What is both possible and impossible at the same time?

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.

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

An express train takes 3 seconds to enter the tunnel which is 1 km long.
If it is travelling at 120 km an hour, how long will it take to pass completely through the tunnel?

What's the only room from which no one can enter or leave

Why is the longest human nose just 11 inches?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

By using 'because' continuously three times, can you make an English statement ?

In a Society, there are over 100 flats.

Flat 1 is named the first flat.
Flat 2 is named the second flat.
Flat 3 is named the third flat. And So On.....

A visitor decides to walk through all the flats, and he finds all the flats except flat 62.
Anmol later founds that the locals of the town have given it another name.

What is the name of the Flat?