CFS/CRFS are reformulation of which already present terms?

CFS/CRFS are by definition sets of (sets of) forces. In other words, it's just a shuffling around of force-terms, nothing more.

From which already known axiom/premise, this can be derived?

Those of Newtonian mechanics.

To be precise, my CFS/CRFS are based on my Instantaneous Law of Inertia.

(Please forgive the typo in my original post: "I cannot allow the derivation" should read "It cannot allow the derivation".)

Which is based purely on Newtonian mechanics, and nothing more (at least, you haven't demonstrated otherwise). So no new axiom or premise here!

Did I claim that, my model is better than Newton's?

As far as I know, Newton didn't claim his theory was a TOE, but you do. So yes, yes you do.

I observe some similarity between my approach and Lagrangian model. Trajectory of a particle is considered in both these models.

(No comment.)

Did Lagrange introduce any new axiom/premise? In my case my Instantaneous Law of Inertia can be considered as a new axiom/premise.

Well, yes. How about the idea of the potential? That doesn't exist as a fundamental object in Newtonian mechanics.

No new physics is introduced by Lagrangian mechanics compared to Newtonian mechanics; following wikipedia.

That is totally true, but that was not what I was saying. They have different starting points, but yours is the same as Newtonian mechanics. Therefore, the situations are quite different.

May be true. People here are not supporting me. Neither they are supporting you.

(No comment, since this isn't a popularity contest.)

I answered your questions in the post #179.

For a change, can you answer my questions in the post #171.

(Note that that post wasn't directed at me, so that's why I didn't answer it. Also, I only see one question there?)

The difficulty is that the two theories seems to be incompatible at a fundamental level, at least in their current forms. A more generalized version of both needs to be found, and hopefully those can be unified. But without a discrepancy between observations and theory, it is difficult to figure out what direction to work towards.