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

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

What are the next two letters in the following series and why?
W A T N T L I T F S _ _

*Hint: Check Puzzle Title

Write the next letter in this sequence.
O, T, T, F, F, S, S, E, __
**Hint: It is a Number Series Puzzle

How can you make number one disappear by adding something to it?

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

If you read clockwise, you can form a word by inserting three missing letters in the picture given below. Can you do it?

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

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?