The observable universe is constantly expanding as the passage of time allows light to reach us from more and more distant parts of the universe. So it’s less “we don’t know what’s outside” and more like (to a certain extent) “we have to wait and see.” And there’s nothing we’ve seen to indicate that these external regions that are being revealed are anything but more of the same kinds of things in our inner region of the observable universe.

The important thing in the balloon analogy isn’t what the balloon is expanding into, it’s just that every point on the balloon is drifting away from every other point.

One thing to consider, though, is that space may not even be a real physical thing. Maybe location is just a property of things, like mass or electrical charge. It could just be an inherent value that adjusts and influences other things according to the laws of physics. Maybe it’s less that “space is expanding” and just that “the location property of everything is constantly diverging.” There’s no need to worry about what anything is expanding into because our conception of space may just be a mental construct.

I would think you’d have to instantaneously accelerate because incremental acceleration doesn’t work the way we typically think it does at high speeds.

If you’re moving at 99.999% the speed of light relative to Earth, anything close to your speed is going to be moving quite slowly relative to you. When you accelerate some more, the change in speed relative to those close things is much larger than the change in speed you experience relative to Earth (it gets smaller and smaller as you approach light speed). But as far as I understand, there’s no such thing as moving at light speed relative to Earth but not relative to other sub-light speed things. You’d have to instantaneously move at light speed relative to everything (every sub-light speed thing).

It’s still an unsettled question if we even do