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I assumed uniform reference frame with anything we observe.

This assumption is false. With a not very powerful telescope and under the right conditions you can see [for example] GPS satellites in Earth orbit. They are circling the Earth, their velocity vector is turning every moment, and thus they are not in a uniform reference frame with respect to us on the ground. General Relativity, not Special Relativity applies. This is confirmed in practice. Microsecond adjustments must be made to the proper time of the satellites clocks or GPS would be too inaccurate to be usable.

If something can be observed, it is inside the same universe and hence the same physics apply to me as they do to the observed object.

I don't really know what this means. If you mean: under the same physical conditions the same physical laws would obtain, OK... this is the heart of your misunderstanding. Take a local frame of reference which appears not to be moving. All the physics within that small local frame is the same. Take another local frame a billion parsecs away. Within that small local frame, the physics within that small local frame is the same as ours. But that does not mean that we see the same physics going on in his part of the universe that we see in ours. Because of the expansion of space, he is accelerating away from us. When we watch what he does, we do not see what he sees. For example, if he were taking a measurement of the signature lines of sodium atoms, it would appear to us that those lines are being seen at wavelengths that are considerably longer than where we see them. IF we make your assumption, we have to account for the fact that what he is measuring turns out to be the same as what we are measuring, even though the numbers are different. And the conclusion we will arrive at is that his part of the universe is moving away from ours at a significant percentage of the speed of light.

If an object is wiggling, it's subject to the General Theory of Relativity, not the Special Theory of Relativity. The Special Theory doesn't apply to accelerated motion.

Can you "wiggle" faster than the speed of light? No. But there are some dodges. Here are some:

Quantum teleportation: The effect of spin flipping in Bell's Theorem Experiments are apparently propagated faster than the speed of light. This is permitted, because a change in quantum states which conveys no information cannot be used to elsewhere violate causality. I am not going to try to explain why this is true; some of the greatest physicists in history have had serious problems understanding it. But it does very much appear to be true. Google No Communication Theorem if you're interested.

Mathematical entities which are non-material: The "superluminal scissors" or "scissors paradox" is an example that has been known for a long time [You have to be careful how you construct the scissors, as the post at link discusses. But as the "caveat" section makes clear, there is no problem with the vertex point of a pair of closing scissors moving faster than the speed of light.] http://math.ucr.edu/home/baez/physics/Relativity/SR/scissors.html

Our universe. Space is expanding pretty much uniformly in all directions. This means that as objects get further away, their relative velocities are increasing. The further they are, the greater the apparent difference. This gives rise to a Doppler affect red shift. The most distant objects are the most red shifted. The most distant objects are those moving away from us at the greatest speed. Far enough away objects would have apparent velocities which exceed c -- if we could see them. we can't. The wavelengths of light they emit are red-shifted to infinity. Events occurring in those regions can never be detected. We are beyond their event horizon [and vice versa.]

In all three cases, the essential dodge is that no information can be transmitted by the superluminal effect. Thus, there is no Loretntz frame that can be use to violate causality.