Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

Suppose we lay down two cups in front of you. One of the cups is filled with tea and the other one with coffee. Now we ask you to take a spoonful of tea and mix it with the coffee. At this moment, the coffee cup has a mixture of tea and coffee. You have to take that mixture (spoonful) and add it back to the tea.

Can you now tell if the cup of coffee has more tea or the cup of tea has more coffee?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

John is asked to stand behind Jacob and Jacob is asked to stand behind John. Both of them feel confused about it and don't know what to do?

But it is quite possible, do you know how?

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

A Car is crossing a bridge 2 miles long. The bridge can only hold 10000 lbs, which is the exact weight of the car. The Car makes it half way across the bridge and stops. A bird lands on the car. Does the bridge collapse? Explain.

It's a protector.
It sits on a bridge.
One individual can see directly through it, while others wonder what it hides.

What is it?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?