Only when you are referring to a specifically named judge that you have identified in your writing. When referring to 'a judge' in the abstract, or 'judges' collectively, it can be in lower case.
Only when his name follows
You capitalize Judge Smith. You do not need to capitalize retired as it is not part of his title.
Actually, it is acceptable to use "Judge (Name of Judge):" The rule is that you always capitalize a person's title.
When it is used as a title the n it should be capitalized. Letter to the Judge
no
No, they are not proper nouns.
Yes, you should capitalize "Chambers" when referencing the chambers of a judge, as it is a proper noun in this context. For example, "Judge Smith's Chambers" would be written with a capital "C."
Yes it should be capitalized. Remember to follow the punctuation that the company in question uses.
You should capitalize it if it is a brand name.
Yes, the word "judge" should be capitalized when it is used as a title before a name or when it is directly addressing a judge. For example: "Judge Smith presided over the case."
That depends on whether you're using the words as regular or proper nouns. If you're referring to supreme court justices in general, without reference to a specific person or court, then there is no need to capitalize. If you're referring to a specific court, such as the Supreme Court of the United States, or the US Supreme Court, as it's known colloquially, you need to capitalize. The same rules apply to justices. If you're referring to US Supreme Court justices in general, apply capitalization only to the part of the sentence that includes proper (specifically identifying) nouns. If you're referring to a particular justice, as in, "President Obama nominated Supreme Court Justice Sonia Sotomayor in 2009," "justice" needs to be capitalized because you are using it as that particular person's title.
Yes. 'Sun' is its name and you capitalize it just as you capitalize anyone's name.