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

I have one of the three numbers: 1, 2, or 3 in my mind. I speak only truth. You can ask me just one question for which I will only reply in yes or no or don't know. What question will you ask from me so that you are able to know the number?

Spot 5 differences in two Christmas tree below:

There is a brick of gold and a brick of iron in a boat (both 10-inch blocks), if they are both dropped into the water which will make the water level higher?

Below, you can see some coding:
January = 1017
February = 628
March = 1335
April = 145
May = 1353
June = 1064
July = 1074
August = 186

Now deciphering the way it has been coded, can you find out how September will be coded?

Find the next number in the series below

21 32 54 87 131 ?

Most people think of me as money. But when they find me in the water, they won’t get any money out of me. What am I?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

Prove that twice of ten is the same as twice of eleven.

You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?