What breaks yet never falls, and what falls yet never breaks?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)

What four weights can be used to balance from 1 to 30 pounds?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

How can you take 2 from 5 and leave 4?

Can you solve below mathematical equation?

2^1234 - 2^1233

What is the end of everything?

Joseph buys three kinds of chocolates for 100 rupees. The first one is priced at 5 rupees, second one at 3 rupees and third one at 0.5 rupees.

If he bought 100 chocolates in total, how many pieces do you think he bought each chocolate?

He does not have any heart but still, He manages to live.
If you kill him, you will eventually die but yet you kill him.
He cannot run, who is He?