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

You can win me and lose me but never buy me
You can not eat me and never want to part with me
I can make you cry or bring you joy
I am not a machine and definitely not a toy
You keep me but i am not forever just yours
You might find me in a case or on a shelf next to a vase
I am hard and i am tall if you bump me i am sure to fall
I am made of different materials and am at many events
If your lucky and fight hard I might be yours
What am I ?

Solve the mathematical equation in the picture below.

A wealthy man lives alone in a small cottage. Being partially handicapped he had everything delivered to his cottage. The mailman was delivering a letter one Thursday when he noticed that the front door was ajar. Through the opening he could see the man's body lying in a pool of dried blood. When a police officer arrived he surveyed the scene. On the porch were two bottles of warm milk, Monday's newspaper, a catalog, flyers, and unopened mail. The police officer suspects it was foul play. Who does he suspect and why?

I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

There are three boxes which are labeled as Rs100, Rs150, and Rs200. One box contains two notes of Rs. 50. The second box contains one note of Rs50 and one note of Rs100 The third box contains two Rs. 100 notes. All boxes are labeled incorrectly.

What is the minimum number of boxes you must check in order to label all boxes correctly?

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

Buy me, smell me or deliver me, I do not change.

Who am I?