Assuming that the Russians hadn't relocated their factories, how would AFV production have been affected on both sides?
Russia would have lost some tank production capacity. Germany would not have won much.
Could the Germans have used captured tank factories to produce their own tanks?
Measurements and tooling was quite different between German and Russian tanks. The Germans captured numerous T-34 and KV-1, and there were efforts to produce "Germanized" versions of them. These plans were eventually abandoned, as the aforementioned differences would have outweighed the advantages to be had. It was, in the end, more effective to keep producing German designs, as German factories would not have been capable of producing Russian designs in appropriate numbers with appropriate effort.
The same would have been true the other way around.
Using the Russian factories to produce Russian tanks (and spare parts) would have aggravated already-existing logistical problems, as there would have been yet more different designs in the field that need to be supplied with parts, and trained crews (both tank and maintenance).
The German war industry was resource-starved at least as much as it was starved for production resources. Capturing the factories does not increase the available steel, fuel, and ammunition.
Did the Germans consider bombing "Tankograd"?
Not to my knowledge, at least not beyond a "thought experiment" stage.
It is a ~2k mile round trip from Moscow, so did they even have the capability?
Not really, no.
At no point of the war did the Luftwaffe have the capacity for strategic bombing. At the strongest point, during the Battle of Britain, they failed to do significant lasting damage to the British aircraft industry, which was right at their doorstep in comparison and could be reached by most aircraft in their (more extensive) arsenal. After the Battle of Britain, the Luftwaffe's bombing capability remained crippled for the rest of the war.
(I am aware the He-177 had nearly that range)
While Germany still held airfields that far forward, there weren't many He-177 in service. And "nearly" doesn't cut it.
There were no fighter aircraft with that kind of endurance, so the bombers would be unescorted for most of their trip. That didn't work well for big combat boxes of B-17; I'd assume a couple of He-177 would fare much worse.
It would have been a stretch, putting resources at risk (which Germany did not really have to spare) for only a slim chance at doing more than temporary disruption.