Can you find a five letter word that is left with only two letters if one is removed?

What does the below image rebus riddle means ?

A red house is made out of red bricks. A yellow house is made out of yellow bricks. And, a blue house is made out of blue bricks. So, what is a greenhouse made of?

Two boys wish to cross a river. The only way to get to the other side is by boat, but that boat can only take one boy at a time. The boat cannot return on its own, there are no ropes or similar tricks, yet both boys manage to cross using the boat.

How?

One fine day, an intellectual man came to the emperor's court with the aim of testing Birbal's wittiness. In order to do this, he challenged Birbal to answer his question and hence prove that he was as intelligent and witty as he was said to be.
He asked Birbal, Do you want me to ask one difficult question or a hundred easy ones?
Since both Akbar and Birbal had had a tough day and were eager to leave, Birbal hastily told the intellectual to ask him a single difficult question.
Intellectual: OK. Tell me what came first into the world, the egg or the chicken?
Of course, the chicken, Birbal replied with a smile.
This time with a note of victory in his voice, the intellectual asked Birbal, How will you demonstrate that?
What did Birbal say?

I have branches, but no fruit, trunk or leaves. What am I?

I am a type of room you cannot enter or leave. Raised from the ground below, I could be poisonous or a delicious treat. What am I?

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

What country can make you shiver?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?