Ok to satisfy my own Autisim I've been looking into the Island -
Nananu-I-Cake
It may be ever so slightly better selected than I thought at first, it looks like it has a minimum of resources like Water etc to support some rough basic agriculture like a heard of sheep (but I will say it looks like it can't support much more than that), a small farm garden, and a Large dwelling for the owners and another for the "staff", access looks to be by a Boat and I can't see any place to build even a small Air Strip for anything other than a small non cargo craft or micro-lite.
The Harbour is listed as "Deep Water" and in this case and from the pictures it looks like it's a 3 fathom or 20ft clearance so enough to get a decent sized coastal cargo ship to dock and offload supplies and there are a few areas that could be used for more personal craft but nothing that would rest on the bottom as that looks rather rocky but things like Dorys, Ribs etc can just land at the beach.
Here is a picture from the sales site showing what I mean -
The main problem I see is there isn't any place for real growth or it would have happened already, On the pictures there is a single track road between the buildings and the dock, it looks like they have a small drop side van and likely a people transporter or quads for day to day traffic around the place.

But if you look at the already settled area you can see that it's about the most choice location on the island for any sort of serious settlement and it looks like they couldn't get more on that location in any way that would work realistically.
Incidentally just left of center at the bottom of that photo you can see the Burn Pile that's how they are doing the waist disposal - thats fine for the number of people on the island at the moment but it wont scale and would need to have a dedicated collection and incinerator cycle on the side of the island that get the most off shore wind or the place will stink. Hell if you look on the fast bottom left you scan see a second smaller pile so they are already reaching the limit of what's on the island now, or they are running a second smaller pile for human waste.
My next big concern here is power generation on the island, from all the pictures I've seen they don't have any self sustaining power generation, it's possible I've missed a wind turbine but it looks like it's run on a Generator so that means costly fuel imports by ship, or sub surface line from the mainland.
But either of those options requires currency that's recognised by the outside world at time of exchange not days or weeks from delivery to payment, currently the Fiji dollar is worth $0.47 and currently in Fiji a gallon of Fuel is $4.87 a gallon, so if they are currently using Diesel (most likely option) it already has to costing a few thousand usd a year to keep the current population going let alone a Tech heavy group, like what this would have to be just on a communications basis.
Looking at the island, if you where planning on building a small large and extended family out of the way location to be self sufficient and isolated it's great but not for anything larger, unless they plan of trading everything into another currency to make it work, they are so close to the Fiji mainland that Police let alone the government wont let them do half the stuff they want to do, a good swimmer can cross the gap.
If anything that proximity makes this even more of a joke for what they envision, I can only think of two locations they could do this with enough infrastructure to do it that's Pitcairn Island and that's a long shot just because of its location and impractical communications, or The Falklands and that's because they have a nice happy location and source of cash from being part of the UK legally but just distinct enough to open financial and legal doors into the global fiscal markets.
I've dusted off some old skills I have to make this of the current island in about 5 minutes, so i wouldnt stand by it too much but it gives you a idea of what is likely the maximum limmit for the island -
You could make other areas habitable on the island but it would be hard to have a connected community, even if you used local resources, and imported ones you couldn't build what they are planning hell you'd have to quarry out that small island just to make a semi decent surface for the existing roads let alone building new ones - there is a reason new roads are not built in the west unless they are absolutely necessary the materials are expensive especially when you are dealing with people who have never driven on unpaved roads on the regular they can do it for a few minutes if pushed but not much longer than that before getting over confident and sloppy and having a accident and that's in a normal car, let alone a Van or 4X4 or quad bike.
This community is doomed to fail just on the percentages, let alone the logistics and no establised island community wants nothing to do with them, as normally they are just happy the way they are.