Is this not yet a Well-Known Fact that astronomers say "we observed it two weeks ago" and We The Laymen know that Great Distances are involved and the event itself happened "long, long ago, in a galaxy far, far away?"
The concept is mind boggling and very humbling due to the time scales involved. We can talk about an event that won't happen (we won't observe) till a thousand years from now although it already happened 6000 years ago by inferring from physical laws. Most of the universe around us is in snapshots from long ago.
It was announced in 2007 that the Pillars of Creation were destroyed by a supernova's shockwave about 6,000 years ago.[8] Because of the limited speed of light, observers on Earth currently see the shockwave approaching the pillars, and will not see the destruction occur for about another 1,000 years
Something I have wondered before, if we lived in a universe in which an observation from essentially any distance was observable near instantaneously would this help or hinder astronomy?
I would say hinder. If we assume that interesting events are distributed equally throughout space (i.e. the universe is uniform) but differ over time (the early universe was obviously different to the current universe) then astronomers currently get to observe a wide range of events throughout both space and time. If events were observed immediately from all distances, then astronomers would only be able to observe current events.
More of a problem: the edge of the observable universe is simply the edge beyond which light hasn't yet reached us. If the universe is flat and infinite (as it currently appears to be) then in a universe with an infinite speed of light there would be no edge to the observable universe. We would see everything, and the whole night sky would shine like the sun. This would seem to be a hindrance.
edit: On the other hand if the universe just wraps around, then... actually I'm not sure what happens, but I guess every ray of light emitted from a star gets absorbed by something, which would still make the Earth (if planets could even exist) far too hot.
Yes. It would be immensely more difficult if we could not look back in time. There would be no microwave background, for example, so no knowledge of the fluctuations in density soon after the Big Bang.
As a comparison, do you think it would be easier for an alien to figure out the life cycle of humans if they could see a few humans at every period of life (like in astronomy) or if they only saw middle-aged humans, but many more of them?
On the other hand, it would be possible to effectively communicate with distant species, who in turn might have existed for a long time and have records of past events.
Well the concept of observation and causality would be broken/meaningless because this would imply an infinite speed of light. Hence there would be no limit to the speed with which information could be transmitted. We would have much more interesting things to worry about, like if and how we could exist.
If this were the case, every single aspect of our world would be radically different. It is an impossible question to answer satisfactorily. It is debatable if life as we know it would evolve in such a universe. Among other things, there might be no relationship between cause and effect. It rapidly becomes impossible to even talk about the consequences of such a setup, we do not have the required vocabulary, nor the cognitive structured needed to even contemplate it.
I don't have a great understanding of relativity, but doesn't general relativity state that things happen relative to the observer's frame of reference. So, in fact, this event did occur either 2 weeks or 4 billion years ago, or anywhere in between, depending on where you're standing?
The only answer you've gotten so far is garbled nonsense ... and I don't want to make similar mistakes. So I'll stay very simple:
1. You don't need general relativity to talk about this. Special relativity (that's special as in "special case") suffices.
2. It's true that in general, you can't talk sense about the idea that two events happened at the same time; in this case, say, that you looking at your watch two weeks ago and the explosion "really" happening were simultaneous.
Relativity is about the perceived passage of time as observed in reference frames traveling at different velocities relative to one another. So it would have happened two weeks ago to someone traveling very (very) fast, but that's got nothing to do with how far they are from the event itself (i.e. where they're standing).
The frame of reference here is not one of location but of relative velocity. You are allowed to account for the distance the light had to travel before it reached you (and you observed the event) in Relativity, just as in anything else as far as I'm aware.