First of all, if I may ask you to double check your quotation tags before posting - there's a handy "preview post" feature next to "submit reply" that might help. As it is, your posts are very hard to read.
Sorry. My bad.
As for your questions, yes you do seem to have the right intuition there. We see other places in the universe as they'd been long time ago, and the hypothetical aliens see the Earth as it had been long time ago as well.
RE: A good example might be the star Betelgeuse in the Orion constellation. While I'm not sure what's the current consensus on the matter, some time ago it was thought that the stars' fluctuation in size might be an indication of it entering the last stages of life before exploding as a supernova.
Since the star is roughly half a thousand light years away, it might've already exploded, but we wouldn't know, and in fact, couldn't know, before the information about the event(photons) reached us.
Thanks.
RE: The thing is, in cosmology, you have to be very careful with what you mean when thinking about "events happening at the same time". Since in principle no event can influence another event before the interaction traveling at the speed of light(e.g.photons, gravity waves) arrives at its destination, does it even make sense to think of aliens 1000 light years away as living in our "now" moment, i.e. 1000 years in the future of the image we're receiving? It's kind of like trying to predict their future -
-Apologies on OT.
I agree. Sometimes I get the thinking that I'm missing something fundamental about time, space and distances. So i refer to analogies, thought experiment and play a little to understand more on how does it function and its limitation besides the obvious reason of "seeing into the past Or time moves forward that past and future may or may not exist at the same rate and "now" is just an illusion". It's like we're observing the past but underneath is the future which hypothetically exist at the same instance with the observer upon layers of event stack at the same rate. I know going any further than this makes no sense at all. And thanks for the insight. Now back to reality. Got to read more on flat ΛCDM Big Bang model.^^