The latest version for TA (Twilight of the Arnor) should be ver 2.04 . At least that is the version I have. Mind you, I purchased the game long before Stardock moved to Steam so I'm able to download it through other channels. So I wouldn't know the version that Steam would have because I don't actually have the Steam version.

I don't play multiverse myself. I don't see the point in doing so. Other players however seem to like to compare scores.

The large circle of a starbase is the starbase's AoE (Area of Effect). Anything within that circle (even tiles partially covered) can be affected by the starbase. The effects are determined by what starbase modules are installed (the availability of which is determined by the starbase type). For example, if you install ship attack assist modules on your starbase, any ship with the the ability to deal damage will have their damage increased if they are within the AoE of the said starbase. The effects of multiple starbases stack. Some players have built many economic starbases near a research capital so they could install research assist modules on starbases to push research of those planets to absurd levels.

I wrote a TA 101 guide a while back to aid players who were used to playing older versions of the game to make the transition to the TA expansion easier. Things like unique tech trees were big changes back then. I tried to make a 2.0 version of the guide a bit later, but I lost focus much too soon. I should try to finish at some point. It at least has a link to the complete old version.

Here is the link to TA 101:
https://forums.galciv2.com/310907/