Since the black hole has infinite brightness near the singularity just below the photon sphere, would the big bang singularity also possess such characteristic?
Click on the image at left (with the horizon grid) or right (without the horizon grid) for an animation of the appearance of the outside Universe as you lower yourself slowly to the horizon. The Universe appears brighter and brighter as you approach the horizon, tending to infinite brightness at the horizon. But again, no one with any sense would do this.
Answer to the quiz question 5: False. You do NOT see all the future history of the world played out. Once inside the horizon, you are doomed to hit the singularity in a finite time, and you witness only a finite (in practice rather short) time pass in the outside Universe.
In order to watch the history of the Universe unfold, you would have to remain outside the horizon, the Schwarzschild surface. One way to watch all the history of the Universe would be to stay just above the horizon, firing your rockets like crazy just to stay put. The Universe would then appear not only speeded up, but also highly blueshifted (probably roasting you in gamma rays), and concentrated in a tiny piece of the sky just above you.