Find the next number in the sequence

1, 2, 6, 21, 88, __?

In a university, a professor gave a set of three problems to the three brilliant students of his class. See the image for the questions.

What seven-letter word has hundreds of letters in it?

What is the next number in this series?

4,12,84,3612....

When monkey rotate the gear, which mark will be hit 1 or 2 ?

The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

What does this rebus photo means?

A Monkey, a squirrel, and an Eagle are racing to the top of the mango tree. Assuming all these animals are in perfect shape, Which animal will reach to Banana first?

A sea diver is a real show-off. He showed everyone that he can hold his breath underwater for 15 minutes.

I went to the diver and told him that I can be underwater for double the time i.e 30 minutes.
He responded that he will give me 100$ if I would be able to do it. I won 100$.

What did I do?

I am a mother. However, I never give birth.

I am a father. However, I never nurse my children.

Wandering is not possible for me, but standing still happens occurs rarely.

Who am I?