Algebra should only be capitalised if it begins a sentence. Otherwise, it is written as algebra!
No. Class should not be capitalized.
When the word is at the start of a sentence.
No, you should not. You should only capitalize a word when it is at the start of a sentence or when it is a proper noun.
Yes, you should capitalize the word after a comma in a sentence.
No.
Not unless it is the beginning of a sentence.
Yes, you should capitalize the word "Corporate" when it is part of a proper noun or title. For example: Corporate Headquarters.
Yes
Yes, you should capitalize the word "scurvy" if it is the first word in a sentence or if it is part of a proper noun or title.
Yes, you should capitalize the word "Figure" when referring to a figure in a paper.
Yes, if you're referring to the concept of Fate as a proper noun, then you should capitalize it. For example, in the phrase "believer in Fate," the word should not be capitalized.
In a title, you should capitalize all words except for short conjunctions like "for," "and," "but," and "or" unless they are the first or last word in the title.