Can i determine the species that’s on a colony ship in stellaris

Looks like, eventually... yes!

Couldn't tell ya what triggers it, though.

Additionally, I found this line in the 00_strategic_resources script file:

influence = {
    accumulative = yes
    AI_category = influence
    max = 1000
    sector_ignore_cost = yes
}

Which seems to explain how Sectors handle the influence cost (They ignore it! Those cheaters!)

And, confirmed by Paradox Developer: https://twitter.com/Martin_Anward/status/737198287254654976

Sectors do not have influence, they ignore influence costs when building. Outposts cost for country in Clarke.

There are a number of technologies you can research that increase the size of the borders around your outposts and colony ships, including

• Galactic Ambitions

• Manifest Destiny

• Propaganda Transmissions (Repeatable)

The Stellaris Wiki entry on borders also says that:

Border spread appears to work volumetrically. That is, as the empire becomes more dense and grows, its borders also appear to spill outward. Removing colonies or frontier outposts from within the empire's well-established borders may affect the outer border unpredictably.

So building additional colonies and outposts in your empire's interior can increase your borders at the fringes.

If you're expanding your empire via frontier outposts, it's worth noting that

Outposts controlled by sectors do not cost Influence to maintain.