Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

You measure my life in hours
I serve you by expiring
I vanish faster when I am thin
and slower when I am thick
The wind is my energy
What am I?

You know three triplets: Frank John and Wayne (need to return your money). Frank always tells the truth while John and Wayne always lie. You meet one of them on the road and can ask him a three-word question.
Which question, will you ask?

Where do fish keep their money?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

One day, all the courtiers from Akbar's court were gathered in the assembly hall when one of them told the Emperor that all his valuables had been stolen by a thief the previous night.
This shocked the Emperor to his core as the place where that courter stayed was the most secured in the kingdom. The Emperor thought that it is not at all possible for an outsider to enter into the courtier's house and steal the valuables. Only another courtier could commit this crime. He quickly called Birbal to identify the thief.
Birbal thought for a while and successfully solved the mystery by identifying the thief in just one statement.
What did Birbal say?

Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation. Conditions: Each must be used exactly once and no other numbers or symbols can be used.

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?