1.
Yes. If x^2 < 1, then x < 1.
examples: (0.5)^2 = 0.25, (0.9)^2 = 0.81
2.
Yes. If x^2 > 1, then x > 1.
examples 3^2 = 9, 1.1^2 = 1.21
Any positive number mutiplied by a number greater than 1 will grow. So if both numbers are greater than 1, the result will be larger than either original number, which will be greater than 1.
Any positive number mutiplied by a number less than 1 will shrink. So if both numbers are less than 1, the result will be smaller than either original number, which will still be less than 1.