What is the Surname of Barbie Doll?

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.

John is the son of Jacob.
So,
Jacob is the_____of John's father?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

You see a boat filled with people, yet there isn’t a single person on board. How is that possible?

How can you tell a raw egg from a hard-boiled egg?

What can you deduce from the following BrainBat?

CRY
LMKI

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?

A boy was locked in a room by some robbers. All that is in the room is a piano, a calendar, and a bed. The room is locked from the outside. What does he eat, drink, and how does he escape and get out?

An ape is trying to climb on a pole that is 60 feet high. Due to the slippery surface, the ape climbs 3 feet in a minute only to slip back 2 feet.

How much time do you think the monkey will take to reach the top of the pole?