1) I think Line 6 has only specifically tested with the Voodoo Labs, so that's the only one they recommend.  While they aren't likely to say this, you aren't going to mess up your ToneCore pedal trying out different supplies, as long as they have the appropriate voltage and polarity.

2) Yes, it's an isolation issue.  That's why a standard wal-wart for each ToneCore works fine.  It's almost certain that any of the other supplies that use a toroidal transformer would also work, but you never know.  There are getting to be more of them available, but they are all pricey.  The Fuel Tank Jr. is cheaper mostly because it has fewer outputs and only at 9V, and in part because it has no auxiliary ac outlet (I also prefer the AC power cable to be removable).  If it fits your needs, I'd say give it a try (but again, Line 6 might not say that).

Hello,

  The Voodoo Labs power supply would be your best bet. Voodoo Labs created this power supply with our pedals in mind so the device outputs enough clean power to handle the intense DSP's inside the ToneCore pedals.

  There may be other power supplies that would work as well. Furman power supplies definitely come to mind. A friend of mine powers at least 3 ToneCore pedals with is Furman and gets no buzzing or noise at all.

  At the moment, i do not believe there are any plans to develop a dedicated power supply for ToneCore.

  Line6Miller