Do photons in interferometer violate the law of conservation of mass? I mean  Mach-Zehnder Interferometer, where light split into two shortest paths. Is light after splitting wave or particle?
Is it a particle? How could one photon change to two?
If the wave, does the sum of the energies of both waves divided by the square of the speed of light equal to the weight of the original photon?

Thank you.
 A: Good question.  You have a correct-but-uninteresting answer in a comment, that a photon doesn't have any mass. The general form of Einstein's equation is
$$
E^2 = (pc)^2 + (mc^2)^2,
$$
which reduces to the more famous $E=mc^2$ for the special case of a particle at rest, with momentum $p=0$. But photons have no rest mass, and so instead the interesting relation is $E=pc = hc/\lambda = hf$: the energy of a photon depends on its wavelength $\lambda$, its frequency $f$, or its color (which are all just different descriptions of the same property).
It is not the case that a single photon's energy is divided along the two paths of an interferometer.  If that were the case you could put near-ultraviolet photons ($\lambda\approx 350$ nm) into the interferometer, observe near-infrared photons ($\lambda\approx 700$ nm) in either arm, and see near-ultraviolet photons again at the exits. This is emphatically not what happens. If you shine violet light into an interferometer, what you see in the middle is still violet light; there's just less of it in each arm.
But you can also build interferometers for massive particles. Neutron interferometers are interesting because neutrons are typically transmitted at a rate of a few per second, but each neutron spends much less than a millisecond actually in the interferometer — it really is the case that an isolated quantum-mechanical object, with mass and baryon number and a spin and a magnetic moment and all the trimmings, contributes to an interference pattern as if it took two paths through the same interferometer.
If you asked me whether an object in an interferometer is a wave or a particle, I'd hope to say neither; if you held my feet to the fire I'd give in an say "a wave," but then talk more about neutron waves.
A: 
where light split into two shortest paths. Is light after splitting wave or particle? 

One has to define the framework with which to answer what light is. There exists the classical electromagnetic wave given by Maxwell's equations. And there exists the quantum of the electromagnetic wave, called a photon,  in the quantum mechanical electromagnetic framework. The two blend as they are based on the same equations and potentials, except in the quantum framework a single photon has no mass, just spin and energy=h*nu, the same frequency nu of the wave of which it is a quantum.
The frequency "nu" for the photon gives the probability of finding the photon in an (x,y,z,t). The classical wave emerges from a large ensemble of photons into a coherent wave in space and time,with the same frequency nu, which carries information about the energy distribution in space time  of the  classical wave.

Is it a particle? 

an individual photon is an elementary particle, as seen in this double slit sequential experiment.

The frequency pattern builds up in time from the distribution of the photons on the plate. The frequency is the same as if the wave were impinging without photon separation, but as far as the photons are concerned the distribution displays the probability of their scattering from two slits as particles.

How could one photon change to two?

One photon does not split into two without an energy and momentum conserving interaction with an electromagnetic field. It is the classical wave that is being split in the interferometer above, the ensemble of photons is split. 
In a simplified analogy think of the photons as particles in a water flow. An obstacle will separate the flow into two, but the individual particles making up the flow do not split. A photon will go either one way or another depending on the phase.

If the wave, does the sum of the energies of both waves divided by the square of the speed of light equal to the weight of the original photon?

see above .and as the comment in the question says photons have zero mass. In general energy is conserved in all frameworks. The energy of the classical wave is the sum of the energies E=h*nu of its constituent photons.
