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.
More seats available = lower ticket cost. Thus, by booking at the last minute it is very likely many seats will have been booked and the remaining seats (tickets) will have a higher cost. If you want to book cheap domestic flights then you should book at least 1 to 2 months prior to departure date. Also check latest offers on regular basis. Also compare prices on online travel portals because sometimes you will find fare lower as compare on other travel portal.