I'm still trying to understand relativity. Particularly its time predictions about gravity are puzzling.

Suppose we have the following situation:

A planet the size of Earth, approaches a super-massive black hole. After entering the event horizon, the planet is sucked in. As it's falling toward the center, it reaches C (probably), and then keeps falling until it gets close enough that its own gravity begins to have a measurable effect on the singularity.

From that moment, and for another C/distance amount of time, the singularity is being pulled by the Earth's gravity as well, right?

Now, since the acceleration of gravity caused by the Earth's mass is the same for all objects, regardless of mass, doesn't that mean that the super massive black hole will actually gain in velocity, toward the direction the Earth is approaching it from?

Since the Earth's mass is negligible, in terms of momentum, compared to the black hole, the impact won't affect the singularity's velocity much, will it?

So my question: Is this an unbalanced action/reaction. I mean, does this violate Newton's 3rd law? ("For every action, there must be an equal and opposite reaction.")

Is the total momentum of the Earth/ Black hole pair greater after they collide than it was before?

I think what I'm really wondering is how relativity accounts for it all. Certainly the Earth sized object will gain relativistic mass as it approaches the black hole, even though it can only be accelerated up to C. That might add to the force of the impact.

Then, there's the time dilation effect of the singularity. Is the acceleration caused by Earth's gravitational field measured relative to the singularity's time reference? (Which would make it almost zero, or maybe even absolutely zero)?