Taking the resource from the minors though... I thought they could use them. I can tell you I will be "relieving" them of any resources they claim in the future.
They can only not (properly) use the influence resource, it still boosts their IP generated, but as stated above that IP can only be used in an UP meeting and they can't attend those. So basically it's pointless for them.
The other resources do affect them. That said, sucker-punch them in the crotch as soon as you're ready to destroy the base, claim the resource and defend it. No mercy for the weak.
This particular influence has nothing to do with the area shon on the map. It's really nothing more than the numbr of votes you get in the UP. After a vote thios number goes to zero and you start accumulating more again until the next vote.
So while the minors have somthing listed on the trade screen buying any of this will not increase your civ's influence range or help you flip planets in any way.
Completely true, their IP is only useful in the UP vote, I only ask for their IP when I'm buying them out of the game. (Buying their only planet from them, once it turns green, you can ask for all their money and IP to go with it, so might aswell take it.)