The cables simply run through a sleeve which is fixed inside the frame. Cables very very rarely snap in the middle, they're more likely to go at the clamp end if at all, and in any case if they do you simply pull the cable out from the top and from the bottom, and thread a new cable into the slot.
Yes, that's right. You use an outer cable up to the point where it joins the frame, and there is an inner sleeve inside the frame so that you can route the inner through. Where it emerges you put in another outer cable. In this photo you can see where the inners emerge, via a (home made) cable outer stop (the previous owner ran it 1x10) and into the final run of outer cable to the mechs. The cables actually cross inside the frame, so the inner sleeving is absolutely vital!
Another question, how much can the handlebars be raised to give a more comfortable upright ride position ?