They seem connected. There is Piracy going on between some of the routes though, could that be affecting?

Are those starbases connected to your trade network? Mine in game are working correctly.

In my current game I've built three Black Hole Observatories at different systems. However, hovering the Physics Research reveals that I'm only getting +10 production when I figure it should be +30.

I'm new at this game so I'm probably missing something, but could not find any information about it. Would someone here care to explain?

Multiple Black Hole Observatory - Only getting production from one