We know that Finwe was slain by Melkor by the gates of Formenos as the Silmarils were stolen, Then Feanor Rebelled and (stuff happened here) and Finarfin became King of the Noldor in Valinor.
Finwe would presumably have gone to the halls of Mandos for a time of Reflection.
Was he then Reborn into Valinor as described with Finrod? I know Feanor was doomed to spend eternity in Mandos for his actions but Finwe did nothing against the Valar.
If indeed he was reborn, did he retake the kingship?
In the same vain, would Fingolfin have taken the kingship back from Finarfin when he was reborn (as he had the greater claim).
Otherwise Finwe would presumably be subject to his son, even though he is one of the most senior of the Eldar.
I also remember something about Finwe holding himself "Unkinged" while Feanor was banished which may explain why he may not take up the kingship again, however this doesnt apply to Fingolfin.
(ps I know elves are not "reborn" I am using the term instead of "Reembodied or Embodified" :-))