If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

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?

A father told his three sons he would die soon and he needed to decide which one of them to give his property to. He said, “Go to the market and buy something large enough to fill my bedroom, but small enough to fit in your pocket. From this, I will decide which of you is the wisest and worthy enough to inherit my land.” They all went to the market, and each came back with a different item. The father told his sons to come into his bedroom one at a time and try to fill up his bedroom with their items. The first son came in and put some pieces of cloth he bought and laid them across the room, but it barely covered the floor. The second son came in and laid some hay on the floor, but there was only enough to cover half the floor. The third son came in and showed his father what he bought. He wound up getting the property. What did the third son show his father?

After undergoing a successful eye operation, A blind girl has just boarded a train to her home. The doctor asked her to open the bandages after 3 hours. On her train journey, she opened the bandages and within a fraction of the time she commits suicide by jumping off the train.

Though her operation was successful, Why did she commit suicide?

There is something which you can be arrested for attempting but not for successfully completing.

Andrew’s doctor gives him three pills and tells him to take one every half hour. How much time will have passed by the time Andrew’s taken all three pills?

A man looks at a painting in a museum and says, “Brothers and sisters I have none, but that man’s father is my father’s son.” Who is in the painting?

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?