Exactly. The contracts are probably drafted in such a way that allow the end customer (MS/Sony/Nintendo) to pay directly to the fabrication facility to manufacture the chips.
I don't think so. Maybe they thought they could work something out with Intel, but it was a risk. For Sony and MS, it was worth the risk given that the options for a high performance, low power chip that supported 64-bit were limited. Now there are plenty of ARM designs available that can handle this just fine, plus the risk of AMD going bankrupt is so much more now.
Therefore, despite what some people wish the NX to have, going with AMD makes the most sense since no other firm in the world can provide a combined CPU+GPU package at comparable price/performance. I wouldn't be surprised if some elitist PC gamers hate the consoles even more because they don't have Intel+NV parts in them. :hmm:
AMD is certainly capable of doing an ARM design just fine. If Sony or MS does do a future console, I expect it to be ARM too, be it by AMD, Zombie AMD or some other company.
It's easier to just put the contracts and the necessary IP (or access to the necessary IP) under a different entity and spin off as soon as bankruptcy proceedings start. The consoles are a viable business after all and it operates independently from AMD corporate structure.
The new entity wouldn't have the ability to make the chips since it wouldn't have the x86 license.