I have branches, but no fruit, trunk or leaves. What am I?

Can you complete the sequence puzzle?

AR TA GE CA LE VI LI _

If one and a half boys, eat one and a half burgers in one and a half hours.

How many burgers can 9 boys eat in 3 hours?

A father's child, a mother's child, yet no one's son.

Who am I?

There is a shop where written:
Buy 1 for $1
10 for $2
100 for $3
I needed 999 and still only paid $3. How could this be financially viable for the shop-keeper?

Can you divide the below-given shape into four equal and identical pieces?

A deaf and mute man goes to the train station. Tickets for the train are 50 cents each. The man goes to the ticket booth and hands the man inside just a dollar. The man in the booth hands him two tickets.

How did the man in the booth know to give him two tickets without even looking at him?

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

What have one eye but still cannot see?

In the following picture, E is going to slide the object down and as per the terrain and the physics, the round object is going to travel all the way till the end. Now, can you analyze who all people will die when it happens?