Yeah, the marines become the prize crew, AFAIK.
Yes, when the population surrenders, the SYs become yours. Not sure what happens to the ships under construction - they probably become yours as well.
Do note that even when the last planet of an alien empire surrenders, some of their ships might not.
This was the impression I was getting from what I had been looking at, but had not seen anything concrete. If there was no way to get the SY's, they became a high priority target if things started to turn sour on the attack.
As for the ships under construction... well... I was hoped they would get captured, but could completely see it not working that way as well.
If any of their other ships dont surrender, no big deal... With their Homeworld gone, the resistance is effectively broken anyways