double-blind study - an experimental procedure in which neither the subjects of the experiment nor the persons administering the experiment know the critical aspects of the experiment; a double-blind procedure is used to guard against both experimenter bias and placebo effects.
No they get more expensive, airlines will always advise you to book in advance to take advantage of their best fares. Sometimes they do a special deal but not within a week of flying. I would try another airline or make different plans.
As the graph shows, approximately one month in advance is the cheapest time to book, when average savings are at their highest. There is little difference between booking two months in advance and booking on the day of departure, making last minute travel a cost effective option.