Game of Thrones Questions

I noticed that the opening credits seem to show a globe from the inside, rather than outside of the globe. Is there a significance to that? It that why the winters can be years long, or do we just assume its a magic world, not subject to our scientific laws?

Also, how far is it from The Wall, to Winterfell, to Kings Landing, to the Dothraki? How many miles and how many days journey?

Also, a specific episode question from Season Two (or perhaps the beginning of Season 3)

Spoiler:

Theon takes Kings Landing with 20 men. The castle is then surrounded, and he's advised to flee to the Night Watch. He doesn't, makes that speech, and his men knock him out. I assumed the castle was surrounded by Rob's men, and his men turned on him to get out alive. But then we see that Kings Landing has been burned down. Who was at the gate, if not King Rob's men?