Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.

Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statements is a lie.

Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday?

In this image, you can see three almost identical Doraemon images. Can you spot the odd one out from them?

I have holes on the top and bottom. I have holes on my left and on my right. And I have holes in the middle, yet I still hold water. What am I?

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

There are two dice with empty faces in front of you and a marker. You can mark any number on each of the faces of the two dice, but you have to display all 31 days of the month using the two of them.

Which numbers will you mark on which dice so that you can easily depict all the dates of the month?

Twice ten are six of us,

Six are but three of us,

Nine are but four of us;

What can we possibly be?

Would you know more of us?

Twelve are but six of us,

Five are but four, do you see?

What are we?

You have a thousand Re. 1 coins with you. You have ten bags with you and you can put any number of coins in each of the bags. The condition is that if someone asks you for any amount between 1 and 1000, you must be able to give that amount by just giving the bag (you are not allowed to open the bag and give coins).

How will you do it?

Using Only Five 5's and any mathematical operator make sum as 37