These types of puzzles are known as charades. What you have to do is to find two words that are referred to in the first stanza and the second stanza and put them together to form the third word in the third stanza.

Just for example, if my first refers to 'off' and my second refers to 'ice', then my whole will be the 'office'.

My first is present - future's past -
A time in which your lot is cast.

My second is my first of space
Defining people's present place.

My whole describes a lack of site -
A place without length, breadth, or height.

Can you name some countries which do not have the alphabet 'A' in them?

A Scientist was fifty years old in the year 2000 but he was forty years old in the year 2010. How can this be possible?

PS: It has a logical answer.

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...

Can you move 2 matchsticks to form four equal sized squares.

You visit a home for specially-abled children on the occasion of Christmas where you meet with 50 children. You have a box of chocolates containing 50 chocolates exactly.

What if you were asked to one chocolate to each child in a manner that one chocolate still remains in the box? Is it possible?

What can jump higher than a building?

There is something which you can be arrested for attempting but not for successfully completing.

A bomb goes off.
Carnage.
One person, only a few feet away, survives! How can this be?

what does the below rebus mean?