I travel all around the world but always stay in the corner. What am I?

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?

Speaking of rivers, a man calls his dog from the opposite side of the river. The dog crosses the river without getting wet, and without using a bridge or boat. How?

What jumps when it walks and sits when it stands?

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

Can you make the below equation true by using any three numbers from "1, 3, 5, 7, 9, 11, 13 and 15"?

( ) + ( ) + ( ) = 30

We are a group of eight brothers. We consider the weak, yet we protect the king in every battle. If we move ahead, we never turn back. Who are we?

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?

Only one colour, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?