When referring to our Moon you capitalise it, as it is a proper noun.
We saw the Moon in the sky last night. Man first walked on the Moon in 1969.
However, when referring to other moons you do not.
Galileo saw four moons around Jupiter with his telescope.
Whether to use The Moon or the Moon seems open to some debate, however the IAU state that it is the Moon, not The Moon.
no
No.
It's jaywalker, and no.
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No
yes
No.
It is not necessary to do so.
yes
YES
what capitilize it please
No, because it isnot a propernoun.