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

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

Can you spot the man between the coffee bean in the picture below ?

Can you solve the rebus below?

I am never scared but became petrified and can’t live in a house but would die to make one. What am I?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

A man has to get a fox, a chicken, and a sack of corn across a river.

He has a rowboat, and it can only carry him and one other thing.
If the fox and the chicken are left together, the fox will eat the chicken.
If the chicken and the corn are left together, the chicken will eat the corn.

How does the man do it?

Its something that each of us devours,
Not just us but birds, beats, trees, and flowers,
Frets iron and nibbles steel,
Toil hard stones to meal,
Exterminates king, collapse town,
And blows the mountains down.

When it is alive we sing, when it is dead we clap our hands. What is it?