When you are referring to the planet Earth.
At the beginning of a sentence.
in The King ***
No.
No.
yes
No. It's not necessary.
Yes
You do, because they are proper nouns.
If a person is referring to the monarchy system of government, it isn't necessary to capitalise it. However, if the person is referring to the British Monarchy itself, then it is proper to capitalise it.
No, there is no need to capitalise fitness in a sentence.
Greek Mythology or Greek Myth.
You can capitalise it if you want.
Capitalise the cardinal directions when they are referring to a specific region of a country (eg: Northwest America). Do NOT capitalise if they are used as directions (eg: Looking north...).