Can you find out which number multiplied by itself will give the output as 12345678987654321?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

He runs but never walks. Murmurs, but never talks. Has a bed, but never sleeps. And has a mouth, but never eats?

He does not have any heart but still, He manages to live.
If you kill him, you will eventually die but yet you kill him.
He cannot run, who is He?

Two in a corner, one in a room, zero in a house, but one in a shelter. What is it?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

Can you spot what's wrong with the following sentence?

PETER WAS ANGRY AT
HIMSELF BECAUSE HE
ACCIDENTALLY LEFT THE
THE KEYS TO HIS CAR
AT HIS FRIEND'S HOUSE.

In the given picture, you can find two letters missing. When two particular letters are placed in the missing spots, you get an eight-letter word while reading in the anti-clockwise direction. Can you find out the missing letters and the missing word eventually?

My location can be determined by the below rebus.
So where am i ?

In the figure, you can see nine stars. What you have to do is connect all of them by using just four line and without lifting your hand i.e. in a continuous flow.