Special relativity states:
... I'll select and discuss the given statements in some particular order (which may be called "in order of simplicity of discussion") ...
[...] The observer is (anything [...])
Right. Synonymous to "observer" or "anything", in the context of the theory of relativity, there are also the descriptions "material point" or "principal identifiable point" or "participant".
Of particular relevance is Einstein's foundational guideline that:
All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more recognizable material points.
- the identity of distinct recognizable observers in coincidences, and
- the distinctiveness of coincidence events due to different subsets of identifiable observers
are presumed self-evident. Arguably then any such coincidence event is in turn considered observable, and any of its observations (by any particular identified observer) is in turn considered a coincidence (of that observer with the corresponding signal front).
The speed of light [...]
It is to be noted that
In this context of (geometry and kinematics of) the theory of relativity, "light" means any signal front of signals exchanged between observers; and
The statement under consideration is meaningful (reproducible) only as far as the notion of (how to measure) "speed" has been defined (operationally) in the first place.
Einstein expressed this requirement (for the particular notion of "simultaneity") quite memorablý:
We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment whether or not both the lightning strokes occurred simultaneously.
As long as this requirement is not satisfied, I allow myself to be deceived as a physicist (and of course the same applies if I am not a physicist), when I imagine that I am able to attach a meaning to the statement of simultaneity.
(I would ask the reader not to proceed farther until he is fully convinced on this point.)
[...] establish an inertial frame
That's concerning the primary (and especially difficult) method of measurement to be defined (within the General Theory of Relativity):
How to determine whether any two given participants (who were never coincident with each other, but "separated") were at rest to each other?
In other words:
How to establish (joint membership of separated observers together in) one "inertial frame"; if that's possible at all.
Only once this definition has been selected, and the determination of an "inertial frame" did actually succeed, it is possible to speak of (i.e. define and determine) "distance" between participants (or at least: "distance ratios"), "simultaneity" of indications of separated participants, and finally "speed".
The speed of light in a vacuum is always $c$
This statement follows as a theorem, given the usual, suitable definition of "distance between participants $A$ and $B$" as "$c/2$ ping duration", provided $A$ and $B$" were at rest to each other throughout.
(Concretely: the symbolic, literal, non-zero coefficient "$c$" which is part of the distance definition is identified unambiguously as signal front speed; a.k.a. "speed of light in a vacuum".)
The speed of light in a vacuum is always $c$ regardless of the velocity of the observer.
No: this applies only to observers who are involved in the determination of a "speed" value (let's say as "starting gate $A$", and as "finish line $B$") and who were therefore at rest to each other (a.k.a. jointly members of the same "inertial frame", a.k.a. in equal "uniform motion" rather than being individually "accelerated" with respect to some/any "inertial frame").
The laws of physics are the same for all observers in uniform motion.
Certainly the method how to determine whether any given observer had been "in uniform motion", or not, is the same/reproducible (by anyone who likewise understands/uses the basic notions of "identifiable observers" and their "observable coincidences").
The observer is (anything that never travels at the velocity $c$).
any identifiable observer (who could "carry a signal") cannot have been measured travelling faster than the signal front speed $c$, and
members of any two "inertial frames" cannot have measured their mutual speed (of their mutual "uniform motion") as the signal front speed $c$ (otherwise the prerequisite determination of "mutual rest" of observers/participants "within each inertial frames" would have failed in at least case to begin with).
The laws of physics are not the same for anything that does travel at the velocity $c$.
This formulation is confusing anything (observer, participant) which/who is considered observable and identifiable with any "signal itself" (which may be called "nothing but the signal having been exchanged between observers").
But yes, certainly the methods of measurement used by observers, based on their ability of mutually observing and recognized each other's signals, can not meaningfully be "used by signals themselves".
Therefore, conversely, it is in this sense meaningful
that Light and Observers have different laws of physics
However, that's perfectly consistent with RT, derived from "blatantly obvious" notions as sketched above.