Space and time are one thing, which have to be thought about together. Your current thinking imagines that you're in a box, with x, y and z coordinates, and that time is a thing passing inside it. Instead, it'd be more accurate to talk about that you're in a frame of reference with x, y, z and a, and all are tied together. There's no sense in which you can talk about space and not also be talking about time, and vice versa. For a similar idea, a 3d volume is not a plane plus a z axis, where you can talk about moving through just the x and y axis without the z axis mattering. You can talk about a view of that, but it doesn't mean the z axis isn't relevant. Ask two planes not colliding whilst viewed from above how important a z axis is. (Maths jokes are the worst.)
The actual physics involved for discussing this gets absurdly complex very quickly, but this is about as simple as I can think how to explain it whilst still being in the bounds of accurate.
Things cannot "reflect off of the edge of visible universe" because that would require that the light travel back in time which is nonsense.
As of this moment we cannot exclude possibility of discontinuities in the universe which would be cause for example by inflation. But we also have not observed any.