1. If the universe is really a finite size, it likely wouldn't have a real edge, but would just repeat itself endlessly. Since that finite size is at least hundreds of millions of light-years, it might be hard to tell since things change a lot in the hundreds of millions of years it takes for light to get to us.

A concept similar to this was done in L. Ron Hubbard's classic science fiction novel, Battlefield Earth. It does, however, require some sort of instantaneous FTL transport.

The theory behind this is that the image of an event travels outward in an ever-expanding sphere at the speed of light. If you were to position a lens at the appropriate distance (e.g., one light-year to see one year into the past), you would be able to view details of what happened in the past. The lens would need to have a significant amount of reduction, because the surface area of the expanding sphere is huge.

In Battlefield Earth, to discover what happened to the Psychlo homeworld, Johnny and his friends teleport a probe into space at an appropriate distance from the Psychlo world and create a huge gravitational lens to reduce the images. This allows them to see that the planet blew up.

Since we do not have the ability to travel faster than light, however, I don't see how we on earth could view our own past unless the light was somehow bounced back to us. Even then, we do not currently have the ability to pick up details, because our lenses are too small.

Note that the novel Battlefield Earth is much, much better than the movie by the same name.

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