Thoughts on the scale of the universe?

[Tino]

but as far as I can see, the universe seems to be a finite one.

The universe is generally considered to be infinite in size. Think of it this way - you get a starship and you cruise in it way out to the "edge" of the universe where you reach a "wall" of some kind, representing the "end" of the universe. How thick is that wall? What's on the other side of the wall? Since the Universe is by definition everything, the thickness of the wall and everything on the other side of it is still the universe. Whatever "end" you could find, it's still universe on the other side of the end.

there couldn't possibly exist an infinite number of dissections on a line segment, being that it is of finite size (please correct me if I'm wrong).

There's no reason that a line segment can't be infinitely divided, which is what resolves Zeno's paradox. Whatever you think is the smallest possible line segment, I can mathematically divide in half.

Now, by my reasoning, in order for a universe to be infinitely large, it would also have to be infinitely small, as both of these traits are relative attributes.

I'm not clear on what you mean by "infinitely small" but I assume it means that it can be divided into infinitely small segments. As mentioned above, that can be done.