What word does this rebus represent?

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Consider this about a word: The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

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?

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

The horse jumps over the king.
Strangely there is absolutely no scratch on him.

Can anyone explain, how is this possible?

You see a boat filled with people, yet there isn’t a single person on board. How is that possible?

Which number should replace the question mark?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

Can you find the thief by just looking at the picture below?