What goes up but never comes down?

The horse jumps over the king.
Strangely there is absolutely no scratch on him.

Can anyone explain, how is this possible?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

I’m light as a feather, yet the strongest person can’t hold me for five minutes. What am I?

Solve the mathematical equation in the picture below.

I am lying and I always lie. Tell me whether I am lying or telling the truth.

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.

Jack have ten pairs of black socks, eight pairs of white socks and seven pairs of green socks. Everything is mixed in a draw. As there is no light he were not able to identify the colour of the socks. How many of the socks did he want to take to match one pair

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.

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.