No, it is not a proper noun. It is a common noun and does not need to have a cap.
No, "homework" does not need a capital letter unless it is at the beginning of a sentence or used in a title.
The state capital of Montana is Helena. Glacier National Park is in Montana.
No.
Helena is the state capital in Montana.
NO
not really
no
No
The state capital of Montana is Helena.
Helena is the state capital in the U.S. state of Montana.
The abbreviation of units is usually written with a capital letter, if it is based on the name of a person.
The word king does not need a capital letter. The reason the words April, California, and Renae need capital letters at the beginning is that they are proper nouns.