If the 'new' Virgin does survive regardless if VAH files voluntary administration or not will likely be a 1-class domestic LCC or 1-class domestic Hybrid at most. This will fail the criteria for full membership of any full service alliance in general. Not that Alliances are relevant right now, or for the foreseeable future.
Connecting Partner levels are pretty much of limited benefit, pointless and the successor will not likely have many FSC friends apart from bare interlines.
So basically yes, 'VA mk II' will be a domestic carrier in the foreseeable future as Luxon allegedly wanted, but more forming alliances with fellow LCCs in the Asian region. It may even open the sucessor to possibly (re)join the Value Alliance to team up with Scoot, Jeju Air and Cebu Pacific doing the feeding for the VA successor flying into the Asian region once demand recovers from COVID.
Velocity will also likely be sold-off if the investor that gets the VAH assets at administration decides to go the pure domestic LCC route. SIA or Westfarmers may acquire Velocity for the pure reason of absorbing their customer base into Krisflyer or Flybuys with the later having a partnership to the successor before closing Velocity down for good.
Not so sure about that. NZ's 1-class hybrid model on narrowbody aircraft serves them pretty well in Star Alliance and Avianca Brasil joined as a full member as a 1-class domestic only airline. Can't see Velocity being sold off unless Virgin completely collapes. A loyalty programme without an airline attached can't be nearly as valuable and profitable.