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If I recall they got it down to something like a 1kg/second mass.

The only problem was it would annihilate anything in the local area you stopped in, as intergalatic dust that had gathered on the warp bubble, was first converted to trapped high energy rays, and then is spontaneously released upon stopping the warp bubble. They still have a lot of work to do, probably a century by scientific standards (minimum). With narrow general AI they may be able to automate some of the design, simulation, and research and get to a first-principle demonstration in perhaps 30-50 years.

That assumes they solve fusion and are able to greatly increase (two-three orders of magnitude) the efficiency, power, and sophistication of particle accelerators. All the technology needed for a warp drive is gonna follow from this sort of research--including the prerequisites for storing energy in the form of manufactured exotic matter.

Are you some kind of europoor that doesn't have that amount in your back yard?

Speaking of this, if it's traveling instantly then how does time pass around it? Is it truly only the stuff in the craft have no time pass? So if you travel 1 light year, you know that 1 year has passed in the place you came from

I also don't get the part where light travels at the same speed from every perspective. How doesnt light travel faster when my headlights are moving forward with my car? It seems to imply that the light is slowing down in that instance just to match c.

You're thinking of a worm hole. That's another thing all together.
I wrote a shitty explanation for bending space time above that doesn't require punching a hole in space/time.

Think of space like a piece of foam that can be twisted, stretched, or compressed in any or all of its parts.
In this regard, it can be bent by various phenomenon -- most notable of which is gravity.
As an example, photons, which have no mass, and therefore should not be affected by gravity, are still bent around the gravitational lens created by the spatial distortion of a black hole because, from the photon's frame of reference, that straight line it is traveling never changes course, but the 3-dimensional space it is traced across does, just like if you drew a line on the outside of a balloon: the perspective from any point on the line never changes despite any change in the volume of the sphere on which it lies.

In this same respect, imagine a 3-dimensional grid with a ship at its center.
If you were trace its path as a line, but -- using gravity or some equivalent force -- compress the grid ahead of it while expanding the grid inside it, the ship would move through space while not reaching the speed of light, itself, but because the bubble in which it travels is also 'moving' in its own frame of reference, the two combined would allow for a net speed that is greater than either while not violating that universal speed limit on an individual level.
The sum of the whole is greater than the parts.

This is important because the energy required to increase velocity is squared, meaning as you approach the speed of light, you also approach an infinite amount of energy required to increase your velocity that final little bit to c (the same formula also implies that your mass increases the faster your velocity, strangely enough -- you would have infinite mass at c.)
This would make half/near-light travel much more feasible, and possibly lead to faster-than-light, eventually.

It's not traveling through, it's folding and then stepping across the folded space to the destination.