Using Only Five 5's and any mathematical operator make sum as 37

You and your two friends are working in a multinational company. How can you three find out the average salary of you all without disclosing your own salary to the other two?

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

What does the below rebus riddle means?

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

If eleven plus two equals one, what does nine plus five equal?

What does it mean?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?