They are not proper nouns. They would not be capitalized in a sentence.
Yes, "Geology" and "Science" should be capitalized in a sentence because they are proper nouns.
No it shouldn't be capitalized.
Yes, Siamese would be capitalized.
You would only capitalize pelican if it was at the beginning of the sentence. Pelican is not a proper noun, so it would not be capitalized.
Euthanasia is illegal in the United States.
To prevent his sick dog from suffering anymore, he wanted his dog to have euthanasia.
No, "pigeon" is not typically capitalized in a sentence unless it is part of a proper noun or at the beginning of a sentence.
No. It is only if it is at the start of a sentence that it would be.
No. It is not capitalized unless it is part of a formal name.
No, colors are not typically capitalized unless they are part of a proper noun or title. For example, "red car" would not be capitalized, but "Red Cross" would be capitalized.
People do not capitalize "a" in a sentence because it is not a proper noun. There is no other reason why "a" would be capitalized. If you are talking about getting an A on an assignment, however, it would be capitalized.