What is both possible and impossible at the same time?

There are five people. One of them shot and killed one of the other five.
We know following clues:
1. Dan ran in the NY City Marathon yesterday with one of the innocent men.
2. Mike consider being a farmer before he moved to the city.
3. Jeff is a top notch computer consultant and wants to install Ben new computer next week.
4. The murderer had his leg amputated last month.
5. Ben met Jack for the first time six months ago.
6. Jack has been in seclusion since the crime.
7. Dan used to drink heavily.
8. Ben and Jeff built their last computers together.
9. The murderer is Jack's brother. They grew up together in Seattle.

Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?

What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see?

What number when divided in half becomes zero?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

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?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

If an electric train is travelling south, then which way is the smoke going?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

In a particular village, only two barbershops exist.

The first shop has a handsome barber with a neat haircut who is handsomely dressed in clean clothes and is extremely humble with his body language. The place is clean and looks hygienic.

In the second shop, you can find a barber with shabby clothing. His hairs are weirdly cut and his clothes still have the stains from last night's dinner. The place is not clean as well and reeks a bit.

You visit the village for the first time and decide to get your haircut. Which barbershop will you like to go for that and why?