If he accidentally looked at himself without his visor would it hurt him or would he be immune?
According to the Marvel website, they cannot hurt him.
Cyclops' mind generates a psionic field that is attuned to the forces that maintain the apertures. Because this field envelops his body, it automatically shunts the other-dimensional particles back into their point of origin when they collide with his body. Thus, his body is protected from the effects of the particles, and even the thin membranes of his eyelids are sufficient to block the emission of energy.
(Note: Marvel has been historically inconsistent on what the source of Cyclops's blasts are)
On a side note, it's an interesting question as to whether or not a direct shot on the mirror would reflect or just shatter the mirror. There's been some speculation about just what materials Cyclops's beam can bounce off of. The general consensus among fans is that it only works on metal and not on a direct hit, but Uncanny X-men 156 and X-Factor 115 show him bouncing his optic beam off of the ground and into himself and Alex to slow them down (the beams being recoilless, he would not be able to just blast down) with the ground liquefying under the blast even as it reflected it. That would argue that, if the mirror could withstand a direct hit and cause a bounce, it would at least knock Cyclops back with the equivalent force.
All things considered, it's probably easier to take the explanation of "psionic fields" and suggest that Cyclops controls, perhaps subconsciously, what his ability bounces off of and how.
Originally, yes they could hurt him, back when he was created by Stan Lee and Jack Kirby in 1963. Now, for anyone wondering, no, no one ever rebounded one of his beams against him in the original stories. However, it should be noted that on several occasions (The X-Men # 1, The X-Men # 4, & The X-Men # 9 as examples) that when he used his beam at its maximum power output, it caused physical harm, causing him to black out for a brief period. When this happened, the other four X-Men (Iceman, Angel, Beast, & Marvel-Girl) protected Cyclops in his weakened condition, with Beast actually carrying Cyclops around in some stories.