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 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.
Not unless it is preceding a proper noun, acting as a title. i.e, "That person is a judge." as opposed to "That person is Judge Smith."
When it is the name of a particular country, you capitalize it.
Yes. 'Sun' is its name and you capitalize it just as you capitalize anyone's name.
If its a name.