The word "friend" does not need a capital letter unless it is the first word of a sentence or part of a title. In general usage, it is treated as a common noun and should be written in lowercase. However, if "Friend" is used as a proper noun or a specific title, then it would be capitalized.
No, homework does not need a capital letter unless it is the first word of a sentence.
No, "thrush" does not need a capital letter unless it is at the beginning of a sentence or part of a proper noun.
no
not really
No
NO
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.
No
YES
farm
s
No, there is no need for a capital letter after an equal sign in most cases. The convention is to start a new sentence with a capital letter and not necessarily after an equal sign within a sentence.