No it shouldn't be capitalized.
Earth, as in we live on the planet Earth, is supposed to be capitalized. Earth, as in the dirt we walk on, is not supposed to be capitalized.
Usually, yes a phase of the moon is supposed to be capitalized.
Yes. As New York is a proper name, then it would be capitalized in any usage (such as New Yorker).
No, it shouldn't be capitalized.
No it shouldn't be capitalized.
Yes, America should be capitalized.
no
Yes, "Pterodactyl" is supposed to be capitalized as it is a proper noun referring to a specific genus of pterosaur.
No, but the names of individual languages are capitalized.
Yes, Siamese would be capitalized.
Yes.
no