Hey,
1) This can be done through the Pendulum Experiment. There is no air resistance in deep space so if you are travelling in constant velocity, then the pendulum should stay still. If you are accelerating, pendulum should move towards back of space ship and if you are decelerating, pendulum should move forward. Everything moves at a constant velocity till a force is acted upon it. The force is the place the pendulum is tied to. It'll pull it back when you are decelerating ... hope you understand that
2) My text book states (Jacaranda Physics HSC2 pg 82) that "the principle of relativity applies only for non-accelerated steady motion; that is standing at rest or moving with a uniform velocity. this is referred to as an intertial frame of reference. SItuations that involve acceleration are called non-inertial frames of reference".
3) This is the exact next point in the text book same page 82. I don't think you would be able to. From your frame of reference, you are stationary (since you are travelling in constant velocity and no forces are acting on you, back to the pendulum experiment), so you would be thinking you were just hovering in mid air and the whole world is moving the other way. However, we process what actually moves and what doesn't move and conclude that we are moving and not the world. This is my interpretation.
If anyone else has contradictory answers, i'll be glad to hear it. I may possible be wrong
EDIT: CHanged Number 2. We do not work with non-inertial frames of reference so my example was wrong.