You are right on. If you reverse the situation, a being on another planet could be pointing one of these at the earth and just now be seeing the time of Christ walking the earth or Moses, or even further back to the birth of Joan Rivers.
Where they might see Helen Thomas changing her diaper.
Sorry, not so. Because we all began from the same point, the epicenter of the big bang, and have just been gradually drifting apart, we are only as old as the point from which it all began to now. And since we don't really know how fast this expansion was from the epicenter at first, compared to what it is now, we can't calculate how old we are based on the distance we are from the epicenter of the big bang today.
People on that planet are the same age as we are, except (and for arguments sake are moving away in exactly the opposite direction) they're moving in the opposite direction from the point of where it all began than us.
So if they pointed that device at us, light traveling today over x distance isn't the same as the light from say 2000 years ago, because we were moving apart at a faster rate then, as compared to now, but we were much closer together. (yikes!) it would look like we are gradually slowing down, or walking in slow motion. Man It's a good thing i don't so drugs.