What can you deduce from the following BrainBat?

CRY
LMKI

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

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.

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?

In a town, there are over 100 flats.
Flat-1 is named first flat.
Flat-2 is named second flat.
Flat-3 is named third flat.

A visitors 'Victor' decides to walk through all the flats, he finds all the flats except flat-62.
Victor later founds that the local of the town have given it another name.

What is the name of the Flat?

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

A man lives on the fifteenth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator, or if it was raining that day, he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up five flights of stairs to his apartment. Can you explain why he does this?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?