Can you find the key in the picture below?

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?

Rebus Puzzle Definition: A rebus is an illusion device that uses pictures to represent words or parts of words.
What does This Rebus Puzzle Identify?

What begins with T, ends with T, and has T in it?

I am a mother. However, I never give birth.

I am a father. However, I never nurse my children.

Wandering is not possible for me, but standing still happens occurs rarely.

Who am I?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?

What does this mathematical rebus means ?

A man is found dead in his bathroom naked with blood scattered all around him. The bathroom was locked from the inside and there is no trace of any struggle. There is nothing in the bathroom except his pant with the belt still around and his shirt. Also, the medic team can't find any incision in his body that may have been the reason behind so much blood loss.

The Police department is clueless regarding this murder mystery.
Can you?

An express train takes 3 seconds to enter the tunnel which is 1 km long.
If it is travelling at 120 km an hour, how long will it take to pass completely through the tunnel?

The centre of the third figure is empty. What digit should fit inside?