1) Yes. The photon's matter wave is actually its electromagnetic wave.
2) Photon emission is not such a kind of process when you get some particles emitted in some interval of time, and you can assume some emission moment within that interval to every particular particle. No, it is a quantum process. The system's intermediate states are not "some particles are emitted, and some are not emitted yet", but "system has some intemediate probability to be in the initial state, and some probability to be in the final state". Every photon is the subject to that accumulating probability. So the most we can say for every photon is that it is emitted in the same interval of time.
The frequency, polarisaion, direction, spatial distribution and all such characteristics of each photon would be the same as those of the electromagnetic wave. (Some advanced details are omitted.)
3) The same way as you may interpret some particular waveform in different bases, like a function of time or a set of sinewave weights, you can interpret photons in different bases. The non-basic waveform is then understood as a quantum superposition of states that belong to the chosen basis.
4) The question is based on the wrong assumption, see the answer to the question 2.
P.S. You deleted your 4 questions, leaving just one, but I hope my answers would still help you.
Best Answer
Some of my recent results may be highly relevant to your question. For example ( http://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-013-2371-4.pdf - published in the European Physical Journal C, open access; http://akhmeteli.org/akh-prepr-ws-ijqi2.pdf - published in the International Journal of Quantum Information), I showed that the matter field can be algebraically eliminated from the equations of scalar electrodynamics (the Klein-Gordon-Maxwell electrodynamics) in the unitary gauge. The resulting equations describe independent dynamics of the electromagnetic field. Similar results were obtained for spinor electrodynamics (the Dirac-Maxwell electrodynamics) - please see the article in the Eur. Phys. J. C. Therefore, modified Maxwell equations can describe both the electromagnetic field and the matter field.
However, that does not mean that "matter waves are em waves", not always: while it may be true, for example, for electrons and positrons, that does not mean it is also true for, say, neutrons, as strong forces cannot be described by electromagnetic waves, at least I don't know how this can be done. However, there is a possibility that matter waves are a more general gauge field, as it is not obvious that my results cannot be generalized, say, to the Standard Model.