Yes.
Just the word Greek, as you have done.
Capitalize only the G i n Greek but not the mythology. It should be Greek mythology.
You capitalize Apollo because it is a name.
Greek should always be capitalized.
There is only one true god and his his the only that is done in capital letters
because it is a general title given to them it is a common noun not a proper noun
No
You should capitalize Colosseum when referring to the specific ancient Roman amphitheater in Rome.
Ancient Greek
An Ancient Greek is a native or inhabitant of Ancient Greece, the Greek-speaking world of ancient times.
erm... Ancient Greek is from Ancient Greece :P
Ancient Greek