Can you spot what's wrong with the following sentence?

PETER WAS ANGRY AT
HIMSELF BECAUSE HE
ACCIDENTALLY LEFT THE
THE KEYS TO HIS CAR
AT HIS FRIEND'S HOUSE.

The following sentence is false. The preceding sentence is true.
Are these two sentences true or false?

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 ?

What are the next two letters in the following series and why?
W A T N T L I T F S _ _

*Hint: Check Puzzle Title

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.

How many miles does the pigeon travel?

I don't get anymore wetter, no matter how much rain falls on me.

There is so small cabin inside a deep forest.
All the forest burned out to worst possible but the inside of the cabin is still the same.
However all the person inside the cabin die.

How come ?

Solve The below Equation:

ALFA + BETA + GAMA = DELTA

How can you drop a raw egg from a height onto a concrete floor without cracking it?

Before reading ahead, you must know the fact that only one of the people here is telling the truth.

A says that B is lying.
B says that C is lying.
C says both A and B are lying.

Can you find out who is speaking the truth?