No, "narwhal whale" does not need to be capitalized in the middle of a sentence unless it is part of a proper noun or title.
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.
No, it shouldn't be capitalized.
Yes, "Hindenburg" should be capitalized as it is a proper noun referring to the German airship LZ 129 Hindenburg.
No it shouldn't be capitalized.
Yes, America should be capitalized.
no
No, but the names of individual languages are capitalized.
Yes, Siamese would be capitalized.
Yes.
Yes.