You can create a skybox in WED, it will move with the camera but theres still a box. Well I don't know how such a box behaves in A7, I don't use WED anymore :P only lite-c.
1) How do you adjust the size of your skycube if it is created in code? I.e. Entity* sky_whatever{}
You don't, you're not creating a block surrounding the level with sky through lite-c. So if you only used lite-c then you can never bump into your skycube.
2) When you say 'infinite' do you mean you put in 1,600,000 for the level size in WED, or is there some constant representing infinite?
It's a code limit, because an integer only can hold up to around 1,6 mil. After it will count further at the lowest number, which is -1.6 mil. It's written in the manual.
3) Were you in fact adjusting the size of your level in WED, or is there some way to set it in lite-c?
I never ever had to adjust any size in WED, nor is there any way to do so, because there shouldn't be any limits other than visible entities and stuff. But bumping in invisible walls? no.
4) In your space level, are there any objects in it, or just your spaceship?
Yes blocks and models