Theoretically...

If I were traveling at or 99.999999999999999etc% the speed of light, and turned on a flashlight, what would the result be if....

1. I turned it on toward a wall in my direction of travel?

2. I turned it on toward a wall behind me?

3. I shone it out the window of my craft? (Would it appear to bend in one direction or another?)

4. I shone it toward the floor?

And what would an outside observer see?

That's about the only interesting part. You and your flashlight notice and/or do nothing special that you can tell.

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As long as you are traveling at a uniform speed, that is, not accelerating, the answers for your frame of reference are:
1. The light heads towards the wall at c.
2. The light heads towards the wall at c.
3. The light heads out at c with no bending.
4. The light heads for the floor at c.
1. The light heads towards the wall at c.
2. The light heads towards the wall at c.
3. The light heads out at c in a different direction (rotated toward your direction of motion) but still with no bending.
4. The light heads forwards at a slight angle to your direction of motion at c, ultimately hitting the floor.

I know it sounds weird, but that's the way the geometry of spacetime works.

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You are already traveling at 99.9999999999999etc % the speed of light, relative to many distant galaxies.

You would smash into the wall

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PW -- Plant Whisperer

Yep, but you left something out: an outside observer will see the light as having different frequencies:
1. The light heads forward at c but at a much higher frequency (that is, each photon has more energy) and if your flashlight emits a cone of light, the angle of the cone will be much narrower.
2. The light heads towards the rear wall at c but at a lower frequency, with the cone broadened.
For 3 and 4, the frequency will not change because the emission is perpendicular to the direction of travel.
Note that in cases 1 and 2, for such a large fraction of the speed of light we would be talking about (1)high energy gamma rays and (2)radio waves.

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