Regarding Cygnus characters

1&2)
If I were to transfer the parent character to a different server, does the cygnus lose it's blessing? Does the parent character lose it's blessing?

3)
If I were to delete a cygnus character, would the parent character lose his blessing/able to create another cygnus character?

4)
Would the previous cygnus NX have the same cash shop as the cygnus character I would make?

3) Yes/No.
4) No, you'll lose all the NX you have on the cygnus.

I doubt you can use World Transfer with a Cygnus, but I'm not too sure.