Is the gravitational waves velocity also $c$, regardless the adopted inertial frame, and the source movement conditions? The second postulate of STR was made exclusively for light (electromagnetic waves)?
If gravitational waves also travel at velocity $c$, then are they obliged to fulfill this second postulate?
Any wave of field (anti matter, dark matter, dark energy), traveling at velocity $c$, must obey this same postulate?
Since gravitational waves are not contained in the second postulate, does the invariance of these waves need to be proved?
Is Ligo results a proof of the velocity $c$ of gravitational waves?
Can Ligo prove the invariance of gravitational waves?
 A: What you are describing, as well as why electromagnetic waves are constrained to $c$ can be seen as a consequence of STR. Much like time dilation and length contraction the $c$ limit is a result/implication of STR's model Lorentz transformation. 
The same goes for gravitational waves, before General relativity it was a wide point of discussion that a faster than $c$ propagation speed would lead to issues with one of the implications of STR, which is local time. Einstein would go on to prove the propagation speed of $c$ in a very elegant way (proof starts in page six). 
There exists several ways of actually proving this experimentally. One of the first was studying orbital decay rates of binary pulsars that orbit around each other quickly and as such propagate a lot of energy through gravitational waves.
Hope this helps somewhat.
A: It is a misconception that SR second postulate was made for light. In reality, what it says is (local measurement):


*

*particles with rest mass that travel in vacuum with speed less then c will always travel with speeds less then c

*particles with no rest mass that travel in vacuum with speed c will always travel with speed c

*particles that travel in vacuum with speed faster then c will always travel faster then speed c (this part is theoretical)
Now EM waves are quantized, and the particles that make up light are photons, that are massless particles, and they always do travel at speed c in vacuum when measured locally.
Now GWs are theoretically said to be quantized too (there is no experiment to prove this), and the particles that make up GWs are gravitons (theoretical), that are said to be massless particles, that travel at speed c in vacuum, when measure locally.
