Well, AI knows the location of resources without exploring. It also appears to know the location of nearest habitable planet and goes straight for it. It also knows immediately when such planet gets colonized.
With Stellar Cartography, the mini-map tells me the locations of stars and how many planets they have. I just send colony ships to the vicinity and hope that some planets are habitable. Since I play abundant all, there usually are, however if there aren't I just go on to the next system. I assume the AI can do the same thing that I do.
There's no reason to presume prior knowledge of the system on the part of the AI. It seems to me that they always grab the first planet they come to in a system even if it’s a PQ5 that’s right next to a PQ26. I've also seen the AI's have to sit with their ships for a bit if I beat them to a planet. If the AI's have prior knowledge of the system they certainly aren’t using it very well.
The only thing that it’s clear that the AI should have prior knowledge of are the location of anomalies since you can just set your survey ship to auto survey and go straight to unseen anomalies. If you can do this then the AI should as well.
As far as colonizing multiple planets with a single colony ship, I don't believe it's possible. It certainly is possible, as has been pointed out, to colonize and rush build a starport and rush build another colony ship all in the same turn. I know that I can do this in one turn. Given that all the AI movement and production occurs at the same time when you press the end turn button, I don't know how you would know it's the 'same' colony ship unless you made note that it was Colony Ship 1234 on the way in and Colony Ship 1234 on the way out. Have you been able to verify that in your experiment?
It's also possible to see the AI use a colony ship to 'bus' pop to multiple previously colonized planets. This is actually very common because the AI tends to 'claim' planets by colonizing with very low numbers of initial colonists that otherwise take forever to grow.