Q1: the signal is not 'shifted' but scaled. Yes, if 1/a<1 then the resultant would be smaller than the original
Q2: any power of t is symmetrical about the y axis. For any even power, both sides of the y axis will only have positive values for t^EVEN . For any odd power, the negative side of the axis will have negative values for t^ODD and the positive side of the axis will be positive; as they are symmetrical they have the same (but opposite sign) area and consequently adding them together results in zero.