Facing the Sun does not mean looking at it. As there are no air there, you have more light looking directly at the Sun, but LESS light looking somewhat in its direction, but not straightly. Because of that, BTW, you can see stars simultaneously.
Even while looking at the Sun directly, you still could do it for the short time enough for taking a photo, without any real harm.
The spacesuit protects the wearer from cold, heat, extra visible light, UV, soft roentgen, alpha and beta-rays and protons. A bit from gamma-rays. Earth magnetic field is blocking most of Sun alpha, beta rays and protons and also charged energetic cosmic rays. But not from neutrons and gamma-rays. And the spacesuit and even the spacecraft do not protect from them also. So, the space travels remain very dangerous. Space radiation is 50-fold more effective than typical radiation on Earth at causing a type of liver cancer called hepatocellular carcinoma in mice.
Wiki has much info on the space suits history.
The best fiction literature where space suits are impotant is Have Space Suit—Will Travel of Heinlein.