The answer is A. your last name and page number
In the letter particularly, last name usually put as an introduction before the initial content of the letter, so it will be better if created with header.
For page that contains page number, the header is created to give a pointer on what the page number means/indicates
The word FOR in the sentence is used as both C. a preposition and a conjunction.
A is incorrect because a gerund ends in -ing. The word for is neither a noun or adjective or an article (there are only three articles: a, an, the) or a verb, so only C is correct.