in The King ***
Yes
yes
No. It's not necessary.
No.
No.
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.
Greek Mythology or Greek Myth.
When you are referring to the planet Earth.At the beginning of a sentence.
No, there is no need to capitalise fitness in a sentence.
You can capitalise it if you want.