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

What does below chemistry rebus means?

A man had five children. He had $100 with him to give to his children. He decided to start with the youngest child and then give $2 more than each younger child to his next elder child.

For example, if he gives $x to the youngest child, he will give $(x+2) to the next one, $[(x+2) + 2] to the next one and so on.

Can you find out how much did the youngest one receive?

What is the coolest letter in the alphabet?

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

In a stable, there are men and horses. In all, there are 22 heads and 72 feet. How many men and how many horses are in the stable

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

Count the number of squares in the picture below.

What is more useful when it is broken?