What has many keys but can’t open a single lock?

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.

I have branches, but no fruit, trunk or leaves. What am I?

You bought me for dinner but never eat me. What am I?

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

I know a nine-letter word having only one vowel.
Do you ?

A Doctor always sneezes before the rain. Doctor sneezes, Will it rain?

I am a mother. However, I never give birth.

I am a father. However, I never nurse my children.

Wandering is not possible for me, but standing still happens occurs rarely.

Who am I?

We can be boring,Or interesting.
We can be long,Or short.
We can have pictures,Or just words.
Many love us,But many also hate us.
What are we?

A kind heart person buy packed food at 3$/packet from United states and sells them at 1$/packet at Africa. After some time he becomes a millionaire.

How come the guy become millionaire ?