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

What common phrase is represented by the below lines

Easy going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Medium going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Tough going:
Weak, 'I can't do it, I'm staying!'
Tough, 'Let's get going.'

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

You can see it everyday, But cannot touch it at will. What is it?

Transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word!!!

John left on a horse on Thursday , was gone for two days, and came back on Thursday after completing his work. How did that happen?

0 0 0 = 6
1 1 1 = 6
2 2 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

You can use any mathematical symbols in the space provided to make all above algebraic expressions true.