Im a new user

Virgin Atlantic is largely owned by Skyteam airlines (Delta, Air France, KLM), so it's unlikely that Virgin Atlantic would join any alliance other than Skyteam.
Aer Lingus is owned by IAG which also owns British Airways and Iberia, both in Oneworld. It's unlikely that IAG wants Aer Lingus in a competing alliance. There has been talk about Aer Lingus rejoining Oneworld, either as a full member or as a connecting member, but so far nothing has happened.
Doesn't TUI mainly operate charter flights with passengers who have booked both flights and hotels from the in-house travel agency? I don't see any benefits for a charter airline to form an alliance with other airlines; the business model is so different. Furthermore, I don't understand why you only wish to include one of the group's airlines but not the other ones.
Their business model is different from that of airlines within alliances. They set up hubs all over Europe and compete with everyone (like Ryanair or Easyjet). I doubt that any European airline would be fit to be in an alliance with Norwegian; the business model would first have to be changed significantly.
They are already in Oneworld. Why should they switch to a new and untested alliance? It's the only Oneworld airline serving Russia in a meaningful way, so they probably get lots of trafic from Oneworld people who need to visit Russia for one reason or another.
Why join a new and untested alliance instead of one of the existing ones?
Air Italy is largely owned by Qatar Airways, and Qatar Airways is in Oneworld, so it's unlikely that Air Italy would be allowed to join a competing alliance. They might or might not join Oneworld at some point. Qatar Airways has talked about leaving Oneworld, but this talk might just be rubbish.
They air currently in Star Alliance. Why would they leave to join something new and untested?
They have so far refused to join any alliance at all, preferring to have more independence. Why would they change their mind?