Note: whether it be all of space itself or any of space itself or both
space itself can both be moved at literally any speed and also move at literally any speed.

Scientists have observed some instance of FTL speeds, but with particles in fixed environments going only a tiny bit faster. So I doubt it unless we pull off some Mass Effect bullshit.

the particles aren't actually moving with a velocity faster than light

they are entangled particles from one source sent in different directions

then one particle is manipulated the other is changed so long as environmental noise doesn't break the connection

and you can cause something to be transferred from one to the other in similar fashion but depending on distance, because this is a jump, the distance may be covered faster than light could have covered it

but its not really a speed of moving particles. They are really one physical particle not two but we get this paradox because we think about them in spatial analogy

Einstein, Podolsky and Rosen discussed this a while back (they though they disproved QM by deriving such a paradox but then people did experiment and it was valid)

Today people repeat variations of the experiment but at larger distances and this is possible with all sorts of particles, but really requires massless particles to be optically doable

Yes, but we'll be goo if we're not restructured to proper human anatomical order.
and also lighten the g-force on our frail selves.

Note: whether it be all of space itself or any of space itself or both
space itself can both be moved at literally any speed and also move at literally any speed.

No. Although scientists are now exploring other (purely theoretical) possibilities. like wormholes, space folding and other things. problem is the sheer energy required is insane, and the survival of anything cast in one of these situations highly doubtful.

I still say our best bet is massive ships, cryogeny and a good bit of luck.

There's nothing to say you can't travel faster then the speed of light (when it really should be the speed of electromegnetic radiation, anyway), you just can't travel AT the speed of light...

As soon as two major components are figured out and implemented then I believe it will be possible.

1. An propulsion system that is powered by a self-recharging core that is capable of the necessary power needed for warp speed.
2. An inertial dampening field to prevent the ships' occupants from being killed when gravitation forces are introduced to the spacecraft.

You often hear people say that certain technology is impossible but they can't imagine past today's conventional technology. Just think about how far we have come in the last fifty years technologically...to say or believe that at some point that we will just simply stop discovering things that are currently viewed as science fiction is in itself unbelievable.

so...

no self-powering warp drives are going to exist: excluded by conservation of energy

but quantum teleportation is possible and already done for tiny particles by entanglement. Maybe its can be done for whole people. Only somebody has to go ahead the whole distance at below speed of light and then teleport you to him (or her!) ...