No it shouldn't be capitalized.
Capitalize a geographical term when it is part of a proper noun or a specific location. For example, capitalize "Mississippi River" or "Mount Everest" but not when referring to a general river or mountain.
You should capitalize "American" when referring to the nationality or citizenship of someone from the United States, as in "American citizen." However, you do not capitalize it when referring to general concepts or things relating to America, such as "the American culture."
Capitalize "indictment" when referring to a specific indictment by name or number, but not when used in a general sense. For example, "The Smith indictment" versus "The indictment against the defendant."
In general, you should only capitalize "Will" and "Trust" when they are used as specific legal terms referring to a Last Will and Testament or a Trust document. Otherwise, they should be written in lowercase.
Yes, when referring to a specific region like the North country, it's common practice to capitalize "North" to signify it as a proper noun.
General Counsel
Capitalize "general" when it is part of a proper name (i.e., General Eisenhower) but not when used alone (i.e., Eisenhower was a general). Also capitalize "general" in direct address (i.e., "Good morning, General.") Usually, capitalize a title when it is understood that a particular person is the topic. (i.e., "When will the General be in his office?") I think the article "the" makes the case though I have found no rule to justify my opinion.
If you are talking about it as a field of study you would capitalize it, but if you say I study math in general then not capitalized
Yes. It should be General Electric clock radio.
Yes, as you capitalize everything that has to do with geography, and the Army
Only if it directly precedes the name of the manager in question.
No you shouldn't.
If you're referring to "The" emergency room rather than "An" emergency room, you can consider it a proper noun and capitalize it. In general it is not capitalized.
Capitalize a geographical term when it is part of a proper noun or a specific location. For example, capitalize "Mississippi River" or "Mount Everest" but not when referring to a general river or mountain.
You should capitalize "American" when referring to the nationality or citizenship of someone from the United States, as in "American citizen." However, you do not capitalize it when referring to general concepts or things relating to America, such as "the American culture."
Capitalize "indictment" when referring to a specific indictment by name or number, but not when used in a general sense. For example, "The Smith indictment" versus "The indictment against the defendant."
I see no reason to capitalize it. In general, you capitalize something if it is the name of a single, unique thing (for example, the name of a person or country); or if something is considered sacred or otherwise important. There are a few additional cases when you capitalize something, but I don't see how any of them would apply in this case.