(he's a little snapped right now. also, moment of truth right now in the twilight rp, whether or not he stops. I'm trying to decide which way he would go in character right now because he's pretty unhinged 0_0)
(yeah, he'd have to not know it's happening though, he's pretty damn strong willed and is a little overly paranoid about being tricked, so if he thinks it's not his thoughts he'll just block them the hell out.)
Okay, the first thing would take eons to have any real effect, and be less efficient as a result, it would be better to terraform using direct methods and have a giant moon sized farm nearby which could feed billions of people. As for the second issue, a place as big as a Death Star could hold something like that easily.
It wouldn't just be for the weapon, having space stations that resemble celestial bodies, like the Death Star, can be incredibly useful. They could be for growing food to export to export to accompanying starships, living quarters for a lot of people, communications centers with long range, and so much more!
Maybe. What I would do is make a base code for it, complete with an understanding of the English language, where it would know almost nothing intially, and grow and learn more about the world on its own. In the base code, I would put in the necessary code for it to understand what it's end goal is, and give it the basic tools to learn how to learn so that it may achieve said goal. I have no idea how much space it would actually need, but I would obtain more storage memory as needed until it can spread across the internet.