I think the camera clipping setting should fix this. Increase the end amount to a larger amount however this may result in decreased performance. Alternatively you could use a “background” scene with the sky in it and a moving camera so you won’t run into this problem.
No, outside camera mode, so when you’re using the Scroll button to hover around and edit objects.
Don’t know if there’s a term for it… you can see the (only) camera is next to the plane in the screenshot