With all due respect, you don't have any idea what you're talking about, and should do some research to avoid embarrassing yourself further.
Your arguments with regard to "the law of conservation of momentum" are basically correct, though poorly stated. Maybe it violates conservation of momentum, in which case conservation of momentum is not a real "law" and becomes merely a widely-used approximation. Maybe it's imparting momentum to something but that isn't a thing we thought could have momentum (see: quantum virtual plasma), in which case the "law" is intact but some other aspect of our understanding of physics gets a major overhaul. Maybe it's actually imparting momentum to a real thing, and there's just been some consistent experimental error that failed to prevent or detect this. Maybe it's not actually imparting momentum to anything at all, and doesn't actually produce thrust, and the observed thrusts are all experimental errors.
Your argument regarding xenon drives (more commonly just called ion drives, ion engines, or electric thrusters) is wrong on all counts. There is absolutely no requirement that your exhaust be moving faster than your vehicle (in what reference frame, anyhow?) for a vehicle to accelerate. Indeed, if there were, rockets could never reach orbit; even Low Earth Orbit requires going faster (relative to Earth) than a chemical rocket's exhaust (relative to the rocket). Relative to an observer on Earth, the exhaust of an orbital rocket during its orbital insertion is actually *in the same direction* as the rocket, not away from it. You should read http://www.real-world-physics-....
Even if that weren't true, though, you're *STILL* wrong. The thing that limits ion drives (including xenon drives) is that they have limited fuel. The ionized gases (xenon or anything else) they use as propellant may have extremely low mass compared to the few tons of chemical rocket fuel that a liquid-fueled spacecraft (including satellites) might carry, but there is still a "fuel tank" and it can still run out. When it does, your ion drive stops working, no matter how much electricity you pump to the electric fields. Thus, the maximum amount of impulse (which, divided by mass-over-time, gives the maximum acceleration; integrate that by time gives the maximum velocity) that an ion drive can produce is determined by its fuel capacity... just like a chemical rocket.
"Photon drive" is one of many terms for a "rocket" that gets its impulse from the momentum of photons. Yes, photons have momentum (even though they don't have mass); this is how a solar sail would work. Even just turning on a flashlight technically produces a (undetectably small) thrust in the direction opposite the beam. See https://en.wikipedia.org/wiki/... for more discussion of how one might build a photon drive. The problem with photon drives is that they have crappy energy-to-thrust efficiency. One of the ways people know the EmDrive is not just a photon drive is because, even at its barely-detectable thrust levels, it's still producing vastly more thrust than a photon drive consuming the same amount of power could manage. Still, the concept of photonic propulsion has some potentially useful applications, and has been known for many decades.
The rest of your post I *mostly* agree with, although the apparent violation of conservation of energy (in addition to apparent violation of conservation of momentum) is another reason to be skeptical of the EmDrive. Maybe it's just transferring energy from some other source we don't yet recognize, like the way uranium "spontaneously" produces energy (heat) from nuclear decay, and a few hundred years ago we couldn't even have understood nuclear decay (in the context of our then-current physics knowledge), much less predicted that we would find it in reality, that it would decrease over time, etc. Maybe the energy required to keep the thrust constant somehow increases as the drive itself is going faster, from a given reference frame; this would allow it to keep up with kinetic energy increasing as the square of velocity, but would turn other aspects of physics on its ears. Maybe it's something else. Maybe there really is perpetual motion, free energy, and all our physics knowledge needs a major overhaul. Maybe our whole existence is a simulation and we found a bug in the modeling of contained electromagnetic radiation, who knows?
I approve of the refusal to state that something is "impossible", but bear in mind that scientific research is still *expensive*, and the expected payout from something that seems as unlikely as the EmDrive is quite low, because the expectation of success is quite low and we don't learn much from it failing (as that would be consistent with our current models). Thus all the (relatively) low-budget experiments so far; as long as they produce findings that violate expectations, the expectation of success gets a little greater, and the expected payout increases commensurately, until it's expected to be worthwhile to fund a higher-budget experiment.