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

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?

Peter wakes up daily to pick up his cycle and crosses the border between Spain and France daily with a bag on his shoulder. He is investigated daily by the officials but they don't find anything suspicious.

If we tell you that he is smuggling something what would it be?

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

John: "Hi Teacher, What is your favourite movie ?".
Chemistry Teacher: "Indium Cerium Platinum Iodine Oxygen Nitrogen".
Ten seconds later... John replied I got it.

Do you?

A man wants to cross the pit of fire which is 25 feet in length and he has 2 planks(fire resistant) 19 feet in length. How can he cross the pit of fire alive?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?