But what if your Big Bang was only a local bang among an infinite number of bangs so far apart from one another that the light from any of them would take 100s of billions of your earth years to reach its nearest neighbor. Then, even now, they are all expanding toward each other with no way for any of their passengers to know it. You won't need to worry about a heat death or a cold death, you will have a death by collision and probably some kind of rebirth to follow.
How can it be both finite in size, and have no edges?
To me, it would seem that were it finite, there would be a point at which one would look back, and see the galaxy and clusters that compose the universe; forward would be an expanse of nothingness. But if this isn't the case, then how I can keep progressing forward (presumably forever, as I can't hit an edge) through space, encountering galaxy after galaxy, but it is still finite?
Unless this is like RPG games where the edges wrap.
Or very slightly curved - measurements come with error bars, so we can't be sure if it's exactly flat. Also note that flatness and finite size are compatible in case of non-trivial topology (think of the flat torus - pacman world - which, however, is not isotropic).
How can it be both finite in size, and have no edges?
Good question, but find me the edge of an idealized balloon. Where is the edge of a sphere? As to why you won’t come back, remember that spacetime is expanding faster an faster, and you can only travel below light speed. Mind you that’s just one possibility. The universe at large could be a lot of different things, but as humans were causally disconnected from anything beyond the shrinking observable universe. Shrinking from our perspective at least, because of the aforementioned expansion and speed limit.
It is a running theory that space time could be curved and wrap, or be more traditionally flat, or even be some kind of saddle that means it is still curved but never meets itself again like a sphere does. Recent studies point to it being flat though, if I remember correctly.
All "space" ie the matter-containing 4d part we live in. There are things before and perhaps outside our universe, brains and such, but that is outside "our universe".