[jfengel]

Yes, an object moving backwards in time would fall upwards.

An object moving forwards in time faster than the speed of light would crush everything, not just itself into the earth. Its energy would go to infinity. That's why "warp bubbles" always require exotic matter with negative energy. Negative energy does a lot of things that run counter to how we expect spacetime to behave, which is what leads us to think that it probably doesn't exist (or we'd have observed it by now).

[ohiovr]

Wouldn't the rate of time reversal play a part in to the pressure exerted to the ground? If time were going at 1 second per second forwards we experience an acceleration of 9.8 meters per second per second, if we went 2 seconds per second would we experience an acceleration of 19.6 meters per second per second?

[jfengel]

You might, depending on what "rate" meant.

The reverse case is a simple matter of swapping the T coordinate, t->-t, for the whole universe. Making a local version of it, such that you're going "faster" than the rest of the universe, leaves a boundary condition whose properties are undefined.

[ohiovr]

For something sci fi how about a kind of gradient?