Can you arrange four 9's and use at most 2 math symbols, to make the total 100?

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.

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

Wednesday, Steve and Pam go to a restaurant to eat lunch. After eating lunch, they pay the bill. But Steve and Pam do not pay the bill. So…who does?

Which English verb becomes past tense just by rearranging the letters?

what does the below rebus mean?

What word is pronounced the same if you take away four of its five letters?

Sherlock breaks into a crime scene. The victim is the owner who is slumped dead on a chair and have a bullet hole in his head. A gun lies on the floor and a cassette recorder is found on the table. On pressing the play button, Sherlock hears the message 'I have committed sins in my life and now I offer my soul to the great Lord' and followed a gunshot Sherlock smiles and informed the police that's its a murder.

Why did he think so?

There were three women in all the swimming costumes!
One was happy and the other two were sad!
The happy one was crying and the sad ones were smiling.
Why was this?