I am an odd number. Take away a letter and I become even. What number am I?

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

Our product and our sum always give the same answer. Who are we?

I am the fastest animal but cannot climb the tree. What am I?

Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?

You’ll find me on Mercury, Earth, Mars, Jupiter, Saturn, and Uranus. But never Neptune, or Venus. What am I?

They are three errirs in this question. Can you find them?

John: "Hi Teacher, What is your favourite movie ?".
Chemistry Teacher: "Indium Cerium Platinum Iodine Oxygen Nitrogen".
Ten seconds later... John replied I got it.

Do you?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

You can win me and lose me but never buy me
You can not eat me and never want to part with me
I can make you cry or bring you joy
I am not a machine and definitely not a toy
You keep me but i am not forever just yours
You might find me in a case or on a shelf next to a vase
I am hard and i am tall if you bump me i am sure to fall
I am made of different materials and am at many events
If your lucky and fight hard I might be yours
What am I ?