It depends on the sentence. For example, if the sentence is, "The mayor is in town," it is lower cased, but if it is, "I can't wait to meet Mayor Smith," then its capitalized.
Mayor should be capitalized. It should be-- Mayor Cartwright.
Yes
Yes, Mayor Pro Tem should be capitalized as it is a formal title given to a member of a city council who acts as mayor in the absence of the actual mayor.
Yes, "Lord Mayor" should be capitalized because it is a title referring to the mayor of a city or town.
The word 'will' should be capitalized only when it is a person's name or the first word in a sentence. As a verb or common noun, it should not be capitalized.
No, it's not necessary unless mayor (a title) is used with the person's name.
Yes, Sunday should always be capitalized.
The second word should not be capitalized
As an abbreviation it should be capitalized.
No, the word "smartphone" should not be capitalized unless it is at the beginning of a sentence.
The word "banker" should not be capitalized unless it is at the beginning of a sentence or part of a title.
No, the word "epitaph" should not be capitalized unless it is at the beginning of a sentence or part of a title.