There was a period of time in human history where everything was one solid entity. We advanced to realize that cells compose living things, making cells the building block of the universe. Then we discovered particles, i.e. atoms, and then those became the fundamental constituent of the universe. Then it became nucleus and electron, then protons and neutrons, and currently we've discovered the presence of quarks.
The same is true in the other direction. There was a point where the Earth was flat, and the ocean was the edge of the universe. We created ships, and the Earth became rounded. We created telescopes and the celestial sphere was shattered, however the sun still revolved around the Earth. Then the Earth got placed 150 million km from the Sun, and our solar system was the center of the universe. Now we are merely an average solar system in a spiral arm of one of hundreds of billions of galaxies, with the edge of the universe 14 Billion light years away.
I don't think either of these stops where we are at currently. I think there is smaller and there is larger.
To answer the teleportation question, I don't think you would see any end to the universe, I think you would simply be staring into empty space. I suppose blackness. Nothingness if you prefer. I don't think there would be any boundary to define the end just a continuation of the infinite nothingness that exists at the outer reaches of our universe.