yes
They are not proper nouns. They would not be capitalized in a sentence.
No it shouldn't be capitalized.
Yes, Siamese would be capitalized.
No, they are not capitalized, just as math and geography would not be capitalized.
No, the word "century" is not capitalized unless it begins a sentence. So "thirteenth century" would not be capitalized in the middle of a sentence.
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.
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, "sister" is not capitalized in the middle of a sentence unless it is used as part of the name or title that is capitalized. For example, in "I have a younger sister," "sister" would not be capitalized.
Euthanasia is illegal in the United States.
No. It is only if it is at the start of a sentence that it would be.
No, but if you named the purple amethyst Shelly, then it would be capitalized.
No. It is not capitalized unless it is part of a formal name.