Yes. Yes this is true for everyone although most people dont realize it. The peripheral retina (the part of the eye that detects light) is actually more sensitive to low light levels then the central retina. At night the peripheral retina "sees better" than the central retina.
Yes. The very center of vision cannot receive the lowered intensity of light that appears at night in very low illumination. The peripheral vision can pick these up and you have noticed that. This is normal.
Yep! The rods are in the periphery and are more sensitive to light. The cones are in the center and give better sharpness and color but less light sensitivity.