What does an Island and the letter T have in common?

In a rainy season, one day 3 huge ladies walked under a normal-sized umbrella.
The umbrella is not huge enough to accommodate all 3 ladies yet not a single lady got wet. Why?

The doctor advised his patient to take a tablet after every fifteen minutes. He gave him five tablets in total.

How much time will he take to have all the five tablets?

A man looks at a painting in a museum and says, “Brothers and sisters I have none, but that man’s father is my father’s son.” Who is in the painting?

Give it food and it will live; give it water and it will die.

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.

Cristina leaves home and then she makes exactly 3 left turns and returns home where she found 2 girls wearing the mask.

Who are these two masked girls?

There is a family that live in a round house. The two parents go out for a movie and leave a babysitter to watch their son. They come back and the kid was not there. Some one kidnapped him. The maid said she was cleaning in a corner. The cook said he was making pizza. The babysitter said she was getting a board game. Who kidnapped him.

My friends called me Iron59 because my parents are a chemist and a mathematician. What is my real name?

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?