I shave every day, but my beard stays the same. 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 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

What is the probability of choosing the correct answer at random from the options below?

a) 1/4
b) 1/2
c) 1
d) 1/4

If a zookeeper had 100 pairs of animals in her zoo, and two pairs of babies are born for each one of the original animals, then (sadly) 23 animals don’t survive, how many animals do you have left in total?

What is 3/7 chicken, 2/3 cat and 2/4 goat?

Tell me the Hindi name of a Vegetable which if we remove 1st word will become a precious Stone and by removing the last word it will become a sweet eatable.

In the figure that has been attached to this question, each digit represents a digit. The similar letters carry the same integer value. Can you expose the original digits?

A man embarked on a questionnaire game. He kept asking the same question to whomever he found. The answer each time was different.

Can you guess what the question was?