We can see things moving faster than light

this subject is fascinating. One notion you mentioned seems to be unnecessarily problematic. You said "it's crazy to think that there's a galaxy we're seeing that might not even be in existence anymore". I would actually agree that it is crazy. Though not how you meant it :)
Very strange and not precise is your usage of term "being in existence". I think the problem is purely created by language here. The problem is created by the fact that we in our imagination create a model of "objective" universe. It might be somewhat useful in our daily life, but I don't think it is consistent with any theory of physics other than maybe Newtons... A notion that there is an objective particular moment in time and that everything in that objective universe exist somewhere... I think that contradicts any theory of relativity, which means that there is no such thing as objectivity, things are relative, meaning subjective. So, THE EXISTENCE of a particular galaxy is ONLY IN RELATION to WHO IS OBSERVING THE OBSERVED.
we cannot say anything about a galaxy that is not in existence anymore. If you disagree you can start right now weep for your grand grand children that have already died. As far as our observations go, we observe an existing galaxy and it will continue to exist long long time after we die and we will continue to see it changing. It is RELATIVITY not OBJECTIVITY.
There is no galaxy that has stopped existing! 
(yeah, I know what I have just said)