How many words can a pen with half refill write?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

What does this mathematical rebus means ?

How much will a 38° angle measure when looked at under a microscope that magnifies ten times?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?

How can a man go eight days without sleep?

A family is trapped in a jungle. There is a bridge which can lead them to safety. But at one time, the bridge can only allow two people to pass through. Also, all of them are afraid of the dark and thus, they can't go alone.

Father takes 1 minute to cross, the mother takes 2 minutes, the son takes 4 and the daughter takes 5 minutes. While crossing the time taken will be according to the slower one. How can they all reach the other side in the minimum possible time?

What is the unique property of the following words ?
* Revive
* Banana
* Grammar
* Voodoo
* Assess
* Potato
* Dresser
* Uneven

Can you find out which number multiplied by itself will give the output as 12345678987654321?