Theoretical question on frames of reference

Some friends (all engineers - not scientists) watching Star Trek and discussing the science behind it. Not whether warp drive or aliens or anything like that were real.... No our discussions were on the frame of reference a ship at "warp".

We understand that Einstein's theory of special relativity states that energy and mass are interchangeable, and speed of light travel is impossible for material objects that weigh more than photons. This can theoretically be solved by warping space to move an object instead of increasing the kinetic energy of the object to do so.

Let's say NASA develops a ship using a warp drive. Space time is warped. We want to travel to Jupiter. So we point the ship at Jupiter and press start.

From our pilot's point of reference is he moving? He can see Jupiter getting larger... but would he feel the acceleration....space is moving, but would he simply feel like he is sitting still? If a person was outside of the warped space, would they see the ship move? If space is warped and space is moving the ship, would the ship be red/blue shifted as it passes?

The final question we had was does our pilot have inertia? The question arose from our theoretical pilot stopping the ship.... I argued that as the ship isn't physically moving, and it has no inertia. My friends argued that the space moving supplied inertia to the pilot. Simply pressing stop would cause the ship to pancake.

On a side note... If my pilot dropped a ball out of the ship as it was moving, what would happen to the ball? Would it simply stop in mid-space, would it move in the same path as the ship or would it suddenly feel relativity and be crushed into a very tiny black hole.

Questions: 1. If we are warping space, what does our astronaut feel? Does he feel like he is moving or not?

1. If space is warped, would the ship be red/blue shifted?

2. Does the warping of space supply inertia to our pilot? Or can you simply turn off the warp field when you arrive at your destination....

I know this isn't very scientific... Please don't flame me because of the question.... just trying to get a real answer to a theoretical question.