Mender's replies are, of course, correct: in free fall with no air drag you will experience no acceleration forces, regardless of your distance from the earth.
Wouldn't you experience gravity, and the acceleration due to gravity, about 9.8 m/s/s? I thought so, and seem to be finding some sources to support that. They say that your accelerometer (the generally used kind) would read zero, but only because it is calibrated to ignore 1g, i.e. to read 1 when you're not accelerating w.r.t. the Earth. How could you experience no acceleration forces, yet plummet towards the ground? If there were a shaft through the earth, you'd slow down to a stop and come back again, so how can that not be a body experiencing acceleration?
The questions are a bit "tricky" in that sense, it seems to me. Someone in orbit (which is what you are in freefall in a lift, BTW, only the orbit is part of a zero-width elipse), is accelerating, I thought, since their velocity is constantly changing its direction and perhaps magnitude. Why? Due to gravity. Have I got it wrong?
I must say, I'm not quite sure where that leaves someone in outer space where there is zero gravity: presumably if they used a normal ground-based accelerometer out of an aircraft, it would be reading 1g, but they are again not accelerating (without thrusters). The accelerometer would adjust for earth gravity, and there isn't any.
Bonus question: in question 1, what is the direction of the 1 g measured?
Normally, don't they read + 1 g? In freefall they read 0 g, and pulling up at 9.8 m/s/s they'd measure 2 g.
Even so, that acceleration is relative to something, as far as I can see, and here I'm thinking it's the Earth.
The Earth is rotating, and at the equator the acceleration of a body on it due to that rotational motion is about 0.03 m/s/s. Thanks to that and the longer distance to the centre, you weigh about 0.5 % less.
g at the poles is about 9.78, and at the equator, about 9.83 m/s/s, but relative to the ground, you don't get that acceleration of g until someone takes it away from under you, no?