What goes up but never comes down?

With pointed fangs I sit and wait; with piercing force I crunch out fate; grabbing victims, proclaiming might; physically joining with a single bite. What am I?

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?

The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

Peter wakes up daily to pick up his cycle and crosses the border between Spain and France daily with a bag on his shoulder. He is investigated daily by the officials but they don't find anything suspicious.

If we tell you that he is smuggling something what would it be?

If 1+9+8=1, what is 2+8+9?

One day, all the courtiers from Akbar's court were gathered in the assembly hall when one of them told the Emperor that all his valuables had been stolen by a thief the previous night.
This shocked the Emperor to his core as the place where that courter stayed was the most secured in the kingdom. The Emperor thought that it is not at all possible for an outsider to enter into the courtier's house and steal the valuables. Only another courtier could commit this crime. He quickly called Birbal to identify the thief.
Birbal thought for a while and successfully solved the mystery by identifying the thief in just one statement.
What did Birbal say?

What kind of band never plays music?

Forwards I am heavy, backward I am not. 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.