People put me on the table and cut me but do not eat me. What am I?

I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?

What is the largest number you can write with just 3 digits?

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

Can you decipher these quotes by Albert Einstein?
Blf xzm mvevi hloev z kilyovn lm gsv ovevo lm dsrxs rg dzh xivzgvw.

What is greater than gold but cannot be bought. it can never be sold and can earn if its sought. though it can be broken, it can still be fixed. for by birth it can't start nor by death it is ended.what am i?

Decode the below four famous ciphers:

8P of the SS
1M of the E
1S of the SS
60M in 1H