The answer for the total mass of the Universe?

[PeterDonis]

You mean the universe is actually absolute, but it appears relative to us?

"The universe" is way too vague. The geometry of spacetime and the stress-energy tensor distribution that gives rise to it via the Einstein Field Equation are absolute, yes. But those things have nothing to do with any particular reference frame.

 

[Dale]

Yes, it does because both objects were added with the same velocity so the difference in their velocities don't change.

Exactly. That is how the principle of relativity works. Different reference frames are related by the Galilean transformation which is simply adding the same velocity to everything.

But I'm not talking about their collisions,

Nor am I. I am talking about an arbitrary force acting between them according to Newton's laws.

If we push a box, either the box gained the acceleration of a or the rest masses gained the acceleration of -a as we have experienced

This is false as I showed above. $\vec a \ne -\vec A$ in general.

the total energy must be the same for that two inertial frames

This is not correct. Energy is frame variant. In every frame, energy is conserved. But different frames will disagree on the total energy.

At this point you need to either engage with the corrections that you have received and start learning the physics that you are missing or there will be no point in further discussion. Do not re-assert the mistakes that have already been pointed out to you. If you do not understand why they are mistakes, then ask for clarification on the specific points that you do not understand. But they are in fact mistakes that indicate some misunderstandings of Newtonian physics.