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.
Yes, "Algebra I" should be capitalized because it is the official name of a specific course. The capitalization indicates that it is a formal title, similar to how you would capitalize other subject names like "Biology" or "English." When referring to the course in general terms, however, you might use "algebra" in lowercase.
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.