Depends on your model of quantum physics.

In none of them can information travel faster than light, but that isn't a satisfactory answer, since one half of an entangled pair still has to "know" what happens to the other in order to give the right result from measurements, even though that doesn't let you send information.

In hidden-variable models, you can argue that the experiment outcome is defined "up-front". In the many-worlds model, both sides have both outcomes but the inconsistent ones "cancel out" as they meet, and pilot-wave interpretations are just many-worlds with one configuration picked out as "real".

But in most of the rest, yes, something travels faster than light. That's a common argument against e.g. collapse interpretations.

They entangle next to each other, and they move apart at max the speed of light. you'll have already paid the price for transferring that bit, so to speak.

Information cannot move faster than the speed of light, period.

It is that question that does not have much meaning.

If you observe one of a pair of entangled particles, you will see one of its possible values. Entanglement only means anything when you compare it's value with its pair's value, and that comparison is limited to the speed of light.

So, yes, in a sense quantum entanglement is free of all the causality issues brought by GR. But it does not really exist until the pair can communicate.

So why not communicate via quantum entanglement? Kind of like FTL TCP.

How would you do that? You can't force the entangled photon at the other end of the channel to measure in any particular way. Once you've measured yours, the other one will measure the same, yes - but you don't know what yours will be until you measure, and the probability is 1/2 either way.