The original Xbox One used a Jaguar[0] based chip, which is really quite a different bread than the Bulldozer or Zen micro architectures. (It's closer to what you'd find in a netbook than in a high end machine, minus the custom memory cache/controller setup AMD designed for Microsoft.)

While it's possible they'd switch micro-architectures, if history is any indication, I suspect it's more likely what you'll see is a die-shrink (28nm -> 14nm) combined with higher clock speeds. And hopefully a faster memory controller (I think that's more the bottleneck than raw CPU power). But that's entirely my speculation.

[0] https://en.wikipedia.org/wiki/Jaguar_(microarchitecture)

Yes, Scorpio might possibly include Zen cores. AMD has on multiple occasions stated that one of their design goals has been to design a core than can scale from ultra power efficient embedded applications all the way to high performance. I think their motivation is to consolidate all their efforts into one core.

Now I don't think they will be able to fit 8 zen cores into a Xbox SoC especially since the Vega GPU also have to fit in there, but quad core with 4 logical cores would still probably be better than the existing Puma cores.

No. The architecture is too different.