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.

I hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?

Can you count the number of seconds in a year?

Clue: You need to bother about calculation.

I shave every day, but my beard stays the same. What am I?

Can you name four days which start with the letter 'T'?

Can you find out which options fits best with the missing column?

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

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

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

I came first on earth but second on the heaven.
I also came twice in a week but found just once in a year.
I stay away from months but you can find me in February.

What am I?