One other thing I noticed. What makes you say it would be trying to tear you?
It is simply a different force at 2 points. It isn't trying to rip you apart.
If you were standing on Earth, you would just feel it trying to crush you.
If you were hanging on a rope, you would feel it trying to pull you down/tear you apart.
But the same is true regardless of if Earth is flat or not.
The actual force you want to look at is the sideways force acting on an object.
The centre of your body is pulled straight down, but your sides are not pulled in the exact same direction. Instead there is a slight angular difference. This results in what can be described as 2 separate forces, a force pulling your side down (parallel to the centre of your body), and a force pushing your side in.
But again, this is insignificant.
Yes, this is one effect of gravity, and it explains why air pressure doesn't decrease linearly with altitude but exponentially. Luckily for us, the ground is pushing our lower body back up which keeps us from snapping. And our flesh is also pulling our body together, so that we don't tear in mid-air or if, for example, two people try to pull us apart.
No. It doesn't.
If that was the case, it would do the same as you go underwater, but it doesn't.
Underwater it increases in a roughly linear way.
The difference in the force of gravity between the surface and the 100 km up is a mere 3% or so. Not enough to make a serious drop off in the atmospheric pressure.
The reason it is exponential is because at sea level, if you take a 1 m^2 square slice (and go up with lines which extend from the centre of Earth, so not quite parallel, such that at 100km your 1 m expands to roughly 1.02 m, so a change of roughly 2%, which I'll also ignore due to how small it is), then the weight of the atmosphere it is supporting is roughly 10 204 kg.
If you move up some distance, you now have less atmosphere to support above you, and thus the weight (and thus pressure) is less. As the pressure is less, the mass per unit volume is less and thus moving up the same distance will result in a smaller decrease. As such, the rate of decrease is proportional to the mass of the air per unit volume which is proportional to the pressure. As the rate of change is proportional to the quantity that is changing, it is an exponential.
This is also why it increases in a linear way underwater, and for each roughly 10m down you gain an atmosphere of pressure.
For a column which is 1m^2, 10m long would be 10m^3, or 10 000 L, and thus weighs roughly 10 kg. This means the force would be roughly 98 000 N, or roughly 100 000 N/m^2, which is roughly an atmosphere.
As water is incompressible, the extra weight of the water does not significantly compress it and thus the weight of the column of water remains the same. This means the change in pressure is not proportional to the pressure and thus is linear.