What is both possible and impossible at the same time?

O_er_t_o_

Complete the missing letters of the given word.

Five thieves looted a bank and they ran away in a car. The bank staff informed the police and they began the search of their car in their jeep. They found them on a road and chased them eventually catching them. The light that is used to fill the number plate was broken on the thieves' car. Also, the headlights of the jeep police were not working. How were the police able to catch the thieves then?

Mr Red Lives in the red house.
Mr Green Lives in the greenhouse.
Mr Yellow Lives in the yellow house.

Who lives in the Whitehouse?

What does it mean?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

Three ants are going up a hill, one behind the other. The last ant then says to the other ants, 'There is an ant behind me!'' How come?

What does the below rebus puzzle mean?

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?

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.