Okay, let's try this one more time. First, the ISS is in basically a vacuum, it is not really "in atmosphere" except in the most strict technicality (even though it is in the thermosphere, it is still in an effective vacuum due to how sparse air molecules are at that altitude).

The height of solar activity causes a reduced level of cosmic radiation at the risk of solar flares and emissions, the Apollo missions took place during this time.

To get even to the limit for recommended safe dosage, the van Allen belts would have to be blocking out more than 98.5% of solar radiation before it reaches the ISS.

Now, going off an actual source instead of the children's worksheet you put forth earlier.... https://www.google.com/url?sa=t&source=web&rct=j&url=https://spaceflight.nasa.gov/spacenews/factsheets/pdfs/radiation.pdf&ved=2ahUKEwif4c-liYDuAhVRHs0KHc45DCwQFjABegQIAhAF&usg=AOvVaw3UqQwZWb1qfSAyEbASCNOc

During solar maximum, those aboard the ISS (which again, is not protected by atmosphere, only the belts and the magnetosphere) get exposed to 80 mSv over a 6 month period. This is equal to .4mSv a day.

Now, since the ISS is basically in a vacuum, that means it is not receiving the benefit of atmospheric protection. For your premise to be correct, the belts by themselves have to block over 98.5% of solar radiation. Not the atmosphere, just the van-allen belts.

The radiation curve is going to be asymptotic as you increase in altitude, with dramatic increases as you go up and the vapor pressure of the atmosphere decreases, then it will begin to level out, once you hit the belts it will jump up again but nowhere near as significantly as when rising through the lower atmosphere, finally leveling off once you are outside the belts. For an 8 day round trip during solar maximum, it is totally plausible to aquire less than 50 mSv.

As for your last questions, I assume you are being hyperbolic about "no radiation in space", so I'm going to discard that one. Going from earth's surface to the ISS has you go through the atmosphere, by the time you reach the ISS there is no real atmosphere left but only scattered particles. The atmosphere blocks far more radiation than the van-allen belts, so while at sea level you are protected from the belts and the atmosphere, in the ISS you are only protected by the belts, so the jump from ISS to outer space is less significant in background radiation than the jump from sea level to the ISS.