I read 2 books in June fitting the month's parameters:
#2 ~ whose author has six letters in first or last name.
Dorothy Sayers - Unnatural Death
. The review is here.
#3 ~ that was published in a six year (ex. 1776, 1868, 1967, 2006).
Mary Stewart - Wildfire at Midnight
. Published in 1956. The review is here.