yes
It should only be capitalized if it directly precedes a name.
Oslo is a city, thus it is always capitalized.
Yes it should be capitalized.
In general, the word "figure" should not be capitalized in a paper unless it is part of a proper noun or title.
Yes I'm pretty sure all college majors are capitalized
maybe
The word evolution does not need to be capitalized.
No, coral does not need to be capitalized.
"Occidental" should be capitalized when referring to Occidental College or similar proper nouns. Otherwise, it is not typically capitalized.
No, they should only be capitalized if they form part of a title.
It does not.
It should be capitalized when it is used in place of the person's name. In other words, it shouldn't be capitalized when it is preceded by a possessive pronoun.