When you are writing formally you should, but you dont have to.
Yes, when referring to a specific list of Spelling Words, you should capitalize the term.
no
No.
The way you capitalize other words. If it's at the beginning of a sentence it should be capitalized. If it's not then it shouldn't be capitalized.
In most quotations you should capitalize the first word and the other words necessary; as in any other regular sentence. There is no need to capitalize most words just because they are in quotations.
Words like a, an, and, or.. You should always capitalize "the" in any part of the title such as, The Dog That Killed The Unicorn. Or something.
Yes, the word "starvation" should be capitalized at the beginning of a sentence like any other word.
No, "engineering staff" should not be capitalized unless it is the first word in a sentence or part of a title.
Proper nouns
In the salutation "Good day to you," you only need to capitalize the first word, "Good."
weeping willow
Unless they are proper nouns or begin a sentence, no.