No. I doesn't change the gravity - it changes the mass. It has nothing to do with gravity.
There's barely any gravity in space anyway.
Mass effect fields can manipulate ships so they have zero (or even negative) mass, so FTL travel is possible.
Gravity has nothing to do with it.
Gravity and mass are related, via the bending of space time.
The way the mass effect works is like this - electricity is passed through element zero, which creates a local mass effect field. Presumably, the intensity of the electric current correlates to the magnitude and intensity of the mass effect field. The mass effect field lowers the mass of all objects within the field. How it does this is unknown, but as mass is mediated by the Higgs boson, maybe it somehow influences the Higgs field. It doesn't matter. What does matter is that it fundamentally alters mass-energy equivalence and thus has the effect of raising the speed of light within the mass effect field.
Now, the value of c within the field is higher, and all mass within the field is proportionally decreased. This allows a given application of energy to accelerate a spacecraft that is enveloped in a mass effect field to faster than the speed of light outside the field (c in a vacuum), but still a tiny fraction of the speed of light within the field. Within the field, it would still take an infinite amount of energy to reach the new speed of light, and in doing so the mass of the vessel would likewise approach infinity due to mass energy equivalence. Thus, relativistic effects do not occur, as the vessel is still travelling at a tiny fraction of the new speed of light within the field. It is technically impossible for a vessel in a mass effect field to ever accelerate to the new speed of light, just as it is impossible outside the field.
The main take away point of the mass effect is that within the field, the speed of light is not a constant and thus neither is the rest mass that a given amount of rest energy produces. Energy, however, is still conserved.
Many people here talk crap about mass effect taking liberties with science. But every Sci fi does that. Personally, I think the idea of the mass effect is ****** brilliant. Possibly the most ingenious concept in all of scifi, in my opinion.