I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

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

What runs around the whole yard without moving?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly

In The 1st month of this year(the year 2013), I noticed that the date 13-1-13 (13 January 2013) is special.

This date is special as:

Date * Month = Year.

Can you figure out which year of this century has a maximum number of such dates?

What does below Rebus say?

XLR8

In a football game, Christina defeated Teresa by 2 - 0 but no man from either side scored. How can this be possible?

A man has a barrel filled with oil that weighs 100 pounds, and then he puts something into it. Now the barrel weighs less than 100 pounds. What did he put in the barrel?

Here is a conversation between a couple who both are software professionals.

Husband: Hey! What is your date of birth?
Wife Replied Angrily: It is 591062400
Husband after doing some calculations replied, "Got It".

What is the DOB of the wife?