The science starts to fail at point 3 and 4 depending on your interpretation.
Point 3 says that mass converts to energy and vice versa, this of course is true. Combined with point 4 it however suggests that this can happen arbitrarily, this is where the physics fail, most notably the conservation of momentum. Bad practice, certainly for science-based, but here is the wiki quotation:
Because of momentum conservation laws, the creation of a pair of fermions (matter particles) out of a single photon cannot occur. However, matter creation is allowed by these laws when in the presence of another particle (another boson, or even a fermion) which can share the primary photon's momentum. Thus, matter can be created out of two photons.
So unless you can shoot one pattern of very high energy photons from one side and a second set from the other you can't do this.
Another physics law you are breaking is Heisenberg. You can either know the exact location of a particle or the exact speed. Not both simultaneously. To create matter in a specific configuration at an atomic level you need to know the exact location of the colliding photon. 343
Since you know the velocity of the photon you would be in breach of the uncertainty principle of Heisenberg.
Two more points I would be highly doubtful about, but can't give you concrete evidence for, is whether you can possibly create a (stable) photon pair with a high enough energy to create neutrons and protons. Also at very high energy densities the non-linear regime of electro-magnetic waves will probably become annoying.
Lastely point two might not strictly speaking be true. Some loop holes in quantum entanglement theory might allow for FTL communication (see comment) but as far as I know there is no major consensus about the loop holes in quantum entanglement. To give a gist of it, quantum entanglement is instantaneously (experimentally proven <PERSON>, et. al., Nature). So if you take a pair of particles, quantum entangle them, move one particle to the other side of the universe as soon as the quantum entanglement is broken you will know it instantly on both sides of the universe. If you could do this with enough mass kept in a quantum entangled state you could send messages instantaneously. Of course you should send the mass there in the old fashioned way. Saw this method once already used in a science fiction novel very nicely. 795