What does this Rebus Picture means ?

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.

John and his wife were living in a rural place. On a particular day, John's wife fell ill and he called the local doctor. When the doctor picked up, he said, "Doctor, my wife is ill. She might have appendicitis."

"This can't be possible! I took out her appendix two years ago myself," the doctor explained.

When diagnosed, John's wife was found to have appendicitis. How can this be possible?

I am an eight letter word and I am a computer terminology.
The second, third and fourth letters make an animal.
The fourth, fifth, sixth, seventh and eighth letters make a weapon.
The first, second, third and fourth letters can be taken as an outcome of any exam.
The fifth, sixth, seventh and eighth letter combine to form a high end typing software.

Can you tell who am I ?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?

In the image given, you can find several triangles. Can you count them all?

Look at the below sequence of letters and tell us what the next letter should be:

O T T F F S S ?

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _