I'll try to explain:
At what rate is the earth accelerating?
It is accelerating at 9.8 m/s^2, the average gravitational acceleration we are used to measure. The small differences on g are attributed either to a "slight pull" of the celestial objects, the fact that acceleration is not entirely uniform, "aetheric wind theory" or denied altogether.
Is the rest of the universe accelerating at the same speed?
Yes, this is why earth doesn't collide with other celestial objects. It's not clear how some celestial bodies happen to fall on earth though.
How fast is the earth going?
For us standing on earth, it is stationary. For a hypothetical observer on space, the answer to this question depends on when earth was formed.
Has it surpassed the speed of light?
No, and it never will. Apparently FE'ers believe in special relativity.
What keeps the earth from wripping itself apart from the extream forces on it?
If you subscribe to the idea that the acceleration is not completely uniform, I have no idea. Earth should have fallen apart a long time ago, but then again this is not your ordinary force, it has special properties never verified that prevent this from happening. If the acceleration is the same on every single point (incredible fine tuning), to which forces are you referring to?