system
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human
How far can we possibly see using a telescope (in terms of time and space)?

Question is basically the title plus a little extra. So I've learned in school that if we use a telescope to observe something that's 1 lightyear away, then what we observe is not the thing as it is today but rather how it was 1 year ago. So the farther away the object of observation is, the older the image we observe of it. 

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If this is true, and please correct me if I'm wrong, then given that the universe is 13.8 billion years old and infinitely wide (because it's constantly expanding right?) then what happens if we theoretically try to observe something that's 13.9 billion lightyears away or farther? 

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Since the universe didn't exist before 13.8 billion years ago, there isn't any light that anyone or anything can pick up and observe right? Or is it that we can only possibly see as far as the universe is currently wide, in which case is it really infinite or is it sort of asymptotically infinite? Is it even theoretically possible to build a telescope that could peer across such astronomical distances? 

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And tangentially related this is something that's been on my mind for a while and I'm hoping someone can answer it. Say you teleported to some observatory 200 lightyears away and were able to use a telescope to look back at Earth. Say you could also zoom in enough to see cities. Would you then see the world as it was in the 1800s? Or is this idea itself, barring the obvious outlandish conditions, science fiction?
gpt
You can actually see further than 13.8 billion light years because the universe is expanding. Light travels at the speed of light, which is one light year per year. So the furthest distance that light can travel in the history of the universe is 13.8 billion light years. But in 13.8 billion years, the universe has expanded a lot. The object that the light came from can be more than 13.8 billion light years away. So we can see objects that are now further than 13.8 billion light years away. Taking this into account, the furthest object you can possibly see is about about 50 billion light years away.

In practice though, the universe was opaque in very early times, so when we look at very large distances we just see a uniform "wall". This is the cosmic microwave background. Note that you don't need an exceptionally good telescope to see that far - the limiting factor in telescopes is more about brightness than resolution, and this background is fairly bright.

And yes, if you were sitting at a star 200 light years away, you could see Earth as it was 200 years ago, although you'd need a very very good telescope to get enough resolution.