If it's a title then it should be capitalized. If it's being used in a sentence then only Treasurer should be capitalized.
Yes, it is both a proper name and an official title.
If it is used a title in place of a name, then yes. That would be difficult with this word, however, so usually it would be a reference to a position or status. That will not be capitalized. For example, if you say "John is our treasurer" it would not be capitalized. However, if you manged to use it as a name, like "come here, Treasurer," then it should be capitalized.
Yes, it is both a proper name and an official title.
Have should be capitalized if it is the beginning of a sentence. Summer should not be capitalized.
It should only be capitalized if it forms part of a title.
Yes it should always be capitalized.
Yes it should be capitalized.
As an abbreviation it should be capitalized.
No it should not be capitalized.
The first 'c' should be capitalized.
Yes it should be capitalized.
Yes, it should be capitalized.