Also, I somehow ended up with BOTH Entertainment Networks and Arenas (Not because of tech trading; I didn't even have Universal Translator researched).
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Entertainment Networks are tied to the first tech in the communications/diplomacy tree. For whatever reason, as soon as you research the tech before Universal Translators (xeno communications, I think) you'll have the ability to build either arenas and entertainment networks. I'm *thinking* this is a bug/oversight, as I wouldn't see why they would want to give the Drengin entertainment networks as an alternative to arenas at such an early point in the game. The Xeno Communications tech is the shortest or second shortest time to research on turn 1, I usually get it out of the way early so I can get translators and work on extorting those other weak races.
As far as the influence bug goes, Carri, I have noticed that unless the computer makes a concerted effort to mass their own influence, I have been having a ridiculously easy time flipping planets. 100% of my games in sandbox mode so far with the Drengin have started me with a PQ 4 planet in my starting star system - I ignore this planet with my first colony ship and find a better quality one to colonize. I end up forgetting the thing as I usually find a handful of much better planets fairly close by. Three games now I've had another race colonize this planet, only to flip to me some 4 or 5 turns later in two of those games. One of the games I recall my homeworld did have an influence bonus tile so I used it to build an influence building. That game it seemed like their planet flipped in only a couple of turns of being settled. The third game they brought a constructor in soon after settling and built an influence starbase. At that point, the skull and crossbones went away.