It's not 'zero G'.
You will still be subject to the same 'G' as you would if you were outside the aircraft.
Yes, it is and no, you won't.
Because you are in an aircraft with engines and flight controls you are able to control the arc so that your vertical acceleration is exactley that of gravity. Similarly you can use power to match drag so that your lateral acceleration is also zero.
In freefall (e.g skydiving) you are always under positive G (less than one initially, but 1G once you reach terminal velociy),because you are creating drag in the vertical axis (which is therefore a form of lift), but in the aircaft you are able to put the wing at an angle of attack that is exactley zero G.
Think of it this way, push any harder and you will be under negative G, don't push at all and you be under 1G, so somewhere in the middle must be- 0G.