Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

Can you find out the remainder when 3^300 is divided by 5?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

How can you make number one disappear by adding something to it?

What is the difference between a jeweller and a jailer?

What always comes into a house through the keyhole?

The picture shows the dice results in each couple of throws. If they are actually following a pattern, can you find out the missing one?

What does this below rebus puzzle mean?

A crime was committed at baker street. Ibrahim Dakota who was shot in the stomach was the main suspect. Sherlock questioned the suspect. The conversation started as:
Sherlock: What's your story, Ibrahim?
Ibrahim: I was walking around baker street and suddenly a man from the back shot me. I ran as fast as I could to save my life".
Sherlock: That is enough (and ask the police to arrest him).

Why does Sherlock think he is the murderer?