1. Here meaning the dimensions affected the mass/gravity of gravitic bodies such as stars and planets.
2. Diverted, here meaning in the sense of being amused and entertained in a small way.
3. An easy mistake to make, especially when the store dummy is being performed by a live person.
4. They might be our descendants. When our descendants will have traveled on Faster Than Light ships to new colonies, they will have also gone back in time(5). Having landed on their new world, the colonists' descendants would then evolve forward through time, until they invent their own FTLs, and come to find us, but travelling backwards in time as they do so and thus arriving before their ancestors (us) have left. Hopefully, better FTLs would be developed.
I feel this scenario would explain the Star Trek universe.
5. Like those FTL particles that were rumoured to have arrived at the other iend of their experiment before they were transmitted. What the particles would do if the scientists changed their minds about sending them, I don't know. Perhaps the particles are precognitive and mind-readers as well.